Camera goes into Shut Down Mode & Flashes the Letter H

Canon AE-1 35mm SLR is a manual focus camera EOS is Canon's designation of auto focus EOS stands for Electro-Optical System. The problem you are experiencing is caused by several little things that throws the camera, wind and cocking leaver out of synchronization or simply come to the end of the roll. There is a frame counter window just to the left of the shutter release behind the shutter speed dial. Also if you have just loaded film in the camera it may not be seated correctly check by releasing the rewind button, wind the film back but not all the way and open the camera to restart the film.

Diagram

Did you actually mean shutter release or shutter advance? And to load the film,you need to pull the roll winder upwards. While you pull the winder upwards, it would have a tuck voice and then the back cover would open up. Make sure you have wound the entire roll before you open the back.

I guess it is actually an AE1 and not an EOS, as EOS is a digital camera! You will have to scrap the film in the camera by opening the back and removing the film. Take out the film can, then pull the film off the take up spool press the windback button on the bottom of the camera. This should get it working again. Try a few shutter releases and wind ons before putting a new film in. If you have important images on the film you don't wan to lose just do the above in complete darkness, and wind the loose film back into the can using the knob at the bottom.

Confirm tht DX shows in LCD. If not then press and hold shift button then press ISO so "DX" appears.Open Camera Back. Insert film cartridge, pull film leader out to right and align with red index mark (inside film chamber on right). Make sure there is no slack in leader.Close camera back until lock release snaps closed. Fully depress shutter until film advances to first frame.
Confirm " 1" and film transport show in LCD. If Film is not loaded correctly, "ERR" show on LCD. Open cack and reload film.
Users manual can be downloaded from:
http://www.lensinc.net/manuals/Nikon_N6006L.pdf

Nothing. You pressed the rewind button and the film rewound: it didn't do so "on its own", it just did what you told it to.

Get it developed and put another film in and don't make the same mistake twice.

You can buy a film leader retriever which fishes out the end of the film from the canister enabling you to reload it, but you need to remember exactly which frame you were at. To get it back to the correct position you then set the camera to fully manual and using the fastest shutter speed and smallest aperture, leave the lens cap on and cover the viewfinder and away from bright light you fire the shutter until the counter reads one lower than you were last at (if your frame counter counts down to zero shots remaining). If the subsequent shots don't register exactly with the old shots, the automatic film processing machinery will likely cut into some frames when cutting the negs into strips. You'll also find that a leader retriever costs more than another roll of film and can take some skill to use.

In summary, your Minolta 7000 is behaving exactly as designed and the cheapest fix is to just drop in a new roll of film.

You can check the shutter without film in the camera. Remove the lens and open the film door. You will see the cloth curtains of the shutter in the center. Advance the film lever to **** the shutter and set the speed dial to a slower speed like 1/15. Hold the camera so it is aimed a a light source, (a window will do) and fire the shutter. You should see the light through the shutter for the time duration is is set to. (1/15). If you see the light source, repeat the process going up one speed setting until you reach 1/1000. If you see the shutter open and close as described, then try another roll. After you load the film and close the back door, make note of what the rewind knob is doing as you advance the film. It should spin counter-clockwise each time. That is a easy test to know that the film is traveling in the camera properly. Vary your exposures with the new roll at different speeds and f-stops. You should get exposures, but if not let us know.

The film is either at the end or stuck. The shutter will not release unless the film advance lever has gone all the way and back.
Make a note of the frame counter. Rewind the film and remove it from the camera (When you feel the film to come loose from the receiving spool, stop rewinding to prevent the end of the film to disappear inside the can. This way you can reload it if it was stuck in the middle.) If the film was completely exposed, take it to be developed.
With the empty camera, try to advance the lever and release the shutter. If this works, the problem was the film and not the camera. Everything is fine. If the problem persists, take it to be repaired.
If the film was stuck in the middle, load it again into the camera. With the lense cap on (preferably in a dark room or similar) 'shoot' as many 'empty' frames as you had on the counter plus two more. Finish the film and develop the pictures.
If the film stucks again at the same place, rewind it and develop normally. It was a bad film.
Hope this helped you to solve the problem.

This is not the best solution as it indicates a faulty film back. The film should advance without resorting to activating the film-wind release lever. That is only for intentionally advancing a partially exposed roll of film. Make sure the multi-exposure lever is not engaged and that the counter does advance and the red mark disappears as you advance to an unexposed frame.

No, it is not the battery. My guess is that the film leader did not stay in the take-up spool and is now bunched up around it. Try rewinding the film carefully as you normally would but remember that you are only rewinding a small portion of the length. You can even just open the film door and start over. You will only loose 3 or 4 frames on the roll.

Possibly the film did not go through the camera. If it did, the problem may be the 2nd(or closing)curtain magnet on the bottom of the camera. When the magnet is working the closing curtain of the shutter is held back 1 to 1000 miliseconds-depending on the shutter speed selected by you. 1ms=1/1000 sec. 1000ms=1 sec. You can tell by 1. removing the lens 2.setting the shutter speed to the "B" setting 3. opening the film door and looking through the camera 4. releasing or firing the camera and keeping pressure on the release button. If the magnet is working, the shutter will stay open as long as the release button is kept pressed down. The closing curtain will close as soon as the release button is released. When the magnet fails, both curtains travel across the film plane together and no exposure is made. Sometimes there is corrosion on the magnet where the wires connect. Sometimes there is some foreign substance or object that interferes with the face of the metal unit that attaches to the magnet when the camera is wound. Sometimes the magnet just fails and needs to be replaced. If the magnet checks out OK the problem may be in the circuits that control the release of the magnet. If this is the problem, the camera needs to be looked at by a competent repair shop. Just so you know, new parts are getting hard to come by, but there are tons of used cameras around that parts can taken from. Hope this helps.