Toshiba won't start, no BIOS, and when it does start it crashes...

Hi
I have a Toshiba Satellite laptop, Vista, 3yrs old. Suddenly it rarely starts up-- doesn't even get to the BIOS/post, though everything's running except the monitor and HDD (fan whirring, DVD drive accessed, etc-- just no HDD or monitor).

Checked the RAM, no problem. Power supply, no problem (unless there's a short somewhere inside the laptop).

Maybe 1 in 20 times I can get it to start just by trying over and over again, and then it's fine, though quite slow to load and slow in general. The HDD in particular is accessed more than normal and for longer times. Occasionally it hangs as well.

If it does turn on, it's fine, but slow, as I say. After leaving it on for a while (hours to days), the screen invariably goes to one of these:
1. narrow (pinstripe) vertical lines/stripes in green or other
2. turned-off screen
3. grey screen
4. wakes up from lock to a black screen.

Usually (but not always) the HDD is going strong at this time and I have to turn the whole thing off.

It doesn't appear to be a monitor issue as there is no problem with the monitor when it's running fine. The HDD checks out fine on another laptop, as does the RAM.

So, my clues are:
1. Usually won't post, won't even make it to BIOS, no beeps, nothing (dead screen).
2. 1 in 20 times it WILL do all of the above, and boot fine, but slower than normal.
3. One day it wouldn't start for over 100 times. I unseated a USB slot cord from the motherboard on a whim, and it started right up (this may be the biggest clue!).

Any ideas? Thanks!