Laptop Lagging and Shutting Down

So I have an Advent somethingorother laptop, running vista, which has just started lagging and freezing intermittently. It'll be fine for a while, then all of a sudden it'll lag for maybe ten seconds, everything will freeze up, then everything will be fine again.
And now it has started shutting itself off at random intervals (not when I'm doing anything particularly heavy sometimes, once i was only playing solitaire). It starts up again right away with no worries.

At first I thought it was a heat problem, because I had some similar symptoms a while back when the bearing on the fan went, and I had to replace the fan. But it does both these things when it's cold, and the temperatures are staying low, and nothing's clogged up ... plus it's on a fan tray thing, so ... I'm thinking that's not it.

So then I figured maybe ram? I tried running memtest but every time I try it shuts off again in the middle. Is this indicative of a ram problem?

Thanks to anyone who can offer advice. I love this thing!