Inspiron 1525 won't turn on

For a while now, it has been switching itself off after about half an hour to an hour (I have to remember to plug it in, otherwise I lose everything). I wasn't too concerned with this, as I thought it was just the cheap battery I bought.

This morning I got one of those yellow boxes pop up asking if I had asked a program to start - some registry thing, I think. I hadn't, so closed it down. Then a red box popped up, something about Malware, with AVG (our virus software) on it. My IE closed itself down then - not sure whether it was before or after the red box. I have had bogus AVG boxes pop up before, so I opened up AVG myself and started a scan. It picked up the registry thing straight away, but didn't say it was a virus. My laptop then went off a few minutes later (a bit sooner than usual), but as it was time to go to school, I had to leave it there.

I went to turn it back on when I got home, and it will whirr for a few seconds as if wanting to start, and then just stops. Even if I hold the on/off button down for 10 seconds or more, it just whirrs (green light at side too) for a few seconds and then stops again.

Anyone know what the problem might be? I don't know if it's related to the turning itself off, or the AVG picking something up.

It's about 2 years old, and out of warranty now. I've briefly read that I could take it all apart, but I'm a bit wary of doing that myself!

Thanks for any advice.

Heather