The paper is not feeding correctly. It feeds about a quarter of the way, then seems like it stops pulling or catches on the left side and starts feeding diagonally or crumples because it doesn't seem to be getting pulled properly thru on the right side

Check your paper feeding roller, first clean them

Solution: Cleaning The Paper Feed Rollers (Windows) iP1600

Clean The Paper Feed Rollers (Windows) Instructions how to clean the paper feed rollers. If the paper feed rollers become dirty, they may not be able to properly feed paper due to the feed roller's slippage.
If paper does not feed correctly, perform the following to clean the paper feed rollers:

1. Open the printer properties.
   
   
2. Click the 'Maintenance' tab and click 'Roller Cleaning'.
   
   
   
   
3. Remove all sheets of paper from the auto sheet feeder.
   
   
4. Confirm the following message, and click 'OK'.
   
   
   
   Note: Clicking 'OK' will activate the paper feed rollers 30 times. Thisactivation will take about 90 seconds. Do not perform other operationsuntil this operation has finished.
   
   
5. Confirm the following message, and click 'OK'.
   
   
   
   
6. After the continuous paper feeding operations in step 5 have finished, load three sheets of plain paper and click 'OK'.
   
   
   
   
7. Confirm the following message, and click 'OK'.
   
   
   
   Note: The following message is displayed when the paper is fed and ejected.
   
   
   
   
8. Click 'OK'.

Roller Cleaning is completed.
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The unit does not power on.
(1) Check the power cord
connection.
(2) Check the connection between
the SPCNT board (JPSU1) and
power supply unit.
(3) Replace the power supply unit.
General
errors

If the feed roller in the back wobbles a lot, the end could be broken, but usually I find that something has fallen in the back stopping the paper. The best way to look for something fallen in is to use a flashlight and small mirror.

The printer hardware should even this out when printing. You should also ensure the paper meets the automatic feeder requirements of the printer.
If printing is skewed, feeding multiple pages or jamming, please follow these instructions (use a regular letter size paper to test after doing the steps given below):
Please check to ensure there is nothing obstructing the paper feed mechanism down inside the printer where it is not easily seen. If there is nothing obvious, unplug the printer and remove the paper. Open the front cover and look above the steel rod. You should see a conveyor belt with rubber teeth on it, like a fan belt. Take the bottom part of that belt and move it gently to the left. The cartridges should come out with it. Make sure the cartridges can move fully from one side of the printer to the other. Check also the output rollers on the bottom of the printer for any blockage. If it is jamming under the carrier assembly, you may be able to fix it using the manual feed slot. Turn the printer off. Next take a #10 envelope and feed it through the left side of the paper feed slot (The manual paper feed slot is preferred, but the automatic feed will do if there is no manual paper feed for this printer) until it comes completely through the printer to the back of the exit rollers. Move it up and down and slowly move it over to the right side. If something is stuck under the black guide plate this may work it loose or you may have to feed the envelope through the front rollers and push your way backward (please be careful here).
Next, take a damp warm cloth and clean the rubber rollers in the automatic sheet feeder. Dust may be coating the rollers there and as they become less tacky, they cannot feed paper correctly.
Finally, turn the printer upside down and carefully shake it for 10 to 20 seconds to see if something falls out of the paper feed path. Then plug the printer back up, take your paper out and replace it with a fresh, small stack (about 5 pages) of paper. Quickly bend the stack in an 'S' shape a few times to separate pages. Make sure it is lined up on the right side of the paper feed and the paper guide on the left is snug on the left side of the paper. Then try to form feed again. If that works, then try to print again. 

Sounds like an obstruction of some sort. Have a look on the left side with a flashlight as best you can, and see if maybe a staple or paperclip got lodged in there.

gears below the paper feeding tray are damaged or some dust particle have blocked the gears try to clean it by blowing the dust use normal greece (oily substance) between the gears so that they can move frequently to pull the paper, and if the gears are damaged you have to change the gears.

there were may situation that can help with this trouble,

1- try to see if the trays are seated correctly no bend or twisted
2- try to check the quality of your paper no concave nor convex ( like U or N)
3- clean the feed roller from either side by moistened cloth, ( only on one direction evenly
4- ensure no hindrance on the paper path inside the machine
5- reset the unit once more

let me know if you need some more

1. Turn the printer off and open the access cover.
2. Look for any obstructions in the paper path and remove them if necessary. (It is possible to move the carrier assembly with the power off.)
3. Turn the printer on, load some paper, and press the Form Feed button.
4. Watch the paper as it feeds through and try to determine where the jam is occurring.
5. Check to see if all the rollers are turning.
   
   If all the rollers are turning, there may be something in the feed path that you can't see. Go to step 6.
   If not, there is probably a feed motor or a gear problem and the printer may require service.
   
6. If the paper is jamming under the carrier assembly, you may be able to fix it using the manual feed slot.
7. Turn the printer off.
8. Take a #10 envelope and feed it through the left side of the manual feed slot until it comes right through the printer to the back of the exit rollers.
9. Move it up and down first, and then slowly move it over to the right side. If something is stuck under the black guide plate, this may work it loose.

Your printer is politely asking you to please get a torch, and open the lid of unit and thoroughly check inside all over for a tiny jam of paper or something else. I am willing to bet you will find some jam. I would also switch it off, and wait a while before turning on and printing again. Good luck