Asus N76 - Strange Behaviour...

Hi - hope someone can help.
Bought an ASUS N76NV laptop a couple of years ago. To be honest, it has not had a great deal of use. There have been periods when it has not been used for a couple of months at a time.
I've just recently brought it back out of storage. It starts, runs and shuts-down perfectly. The problem is that it won't 're-start'.
[Running Windows 7 Pro].
If you restart (rather than shut-down) it turns-off but then I get a black screen (not even a post screen). I then have to remove the battery or press on the on/off button (for 10+ seconds) - whereupon it starts perfectly.
This is what I've done.
1. Swapped HDD. Both of them. No joy.
2. Reinstalled Windows (both the original Win 7 Pro 64 bit and a version of Win Home 64). The OSs install okay - but after the first restart - the problem emerges again. Keep in mind that at this start there is no additional software or drivers to conflict - or even any Microsoft updates. Again, no joy.
3. I've gone through BIOS (v214) and altered what I can and then gone back to factory defaults. No joy.
Before being stored - everything worked perfectly. I've added no software or hardware - the fault has just appeared. I'm scratching my head as to what it could be. I've Googled and Googled - but nothing comes up.
There's no screen flicker, no obvious hardware faults. Weird. Really stumped by this - can't even think where to go next. Any advice - very gratefully received!