I have an Akai PDP5016H television recently it will not power on , I have to push power button several times before it comes on , no picture and no sound , Occasional lly it will stay on with the AKAI logo blue screen and then the screen will change to gray or scramble gray. On the upper right corner it it will say" AIR 8" and at the bottom right corner it will say " fill screen" I looked at the power supply for any bad caps but did not see any visibly. I even check the power supply board for loose or crack solder but still did not find any problem , could there be bad capacitors that are bad and still look good visibly? any and all help is appreciated.

There's a good chance you have failing electrolytic capacitors either in the power section or the inverter section or both.
Any caps in these sections that look bulged at the top, or bulged/leaking at the bottom need to be replaced, and in your case you may need to look very closely. Caps that go in these situations are often grouped in pairs or fours.
If you repeatedly turn it off and on, eventually it'll probably stay on, but every time you turn it off, the TV will get harder and harder to start up until one day it just won't.
Sometimes you have to do the opposite to start it up and unplug it for some time and then try again.

If you aren't tech savvy, don't worry, read the rest of this solution and watch the videos.

If you are handy with a soldering iron and can identify the power supply and inverter / FM section for the backlights, an inexpensive handful of capacitors will likely fix you right up.
Match the capacitance on the capacitors. Go over voltage if you can, and still have them fit.
IE - it's not a bad idea to replace a 10V cap with a 16V or 25V or even a 50V, but don't replace a 680uF cap with a 500uF or a 1000uF (unless you are positive it's only doing ripple filtering, and even then, you should go OVER, not under the uF rating).

Most of the caps that go are 10V 1000uF or 3300uF.

I found some great videos of the procedure (for many Samsungs with the same issue) on youtube.

http://www.youtube.com/watch?v=Mm51C_RDIZE
http://www.youtube.com/watch?v=BNHHrgX_6cs&feature=related
http://www.youtube.com/watch?v=8l0AUj8QUkg&NR=1&feature=fvwp
http://www.youtube.com/watch?v=Y7b_nTaZYcU&feature=related

As you can see, this issue spans plasma TVs, as well as large and small LCD TVs and monitors.
The parts are cheap, and skill required is minimal.