I would also highly recommend
Amnesia: The Dark Descent however given your computer's hardware limitation's I'm not sure if it will run at a decent enough rate to really get into. Try the demo just to see if it will run on your computer. If not I would recommend the developer's other game
Penumbra: Overture which is a 3D puzzle adventure game with a little bit of combat (it sucks and really should be avoided if you can). As for a point-and-click adventure game with a horror theme... if you can find a torrent for the old
Clocktower series you'd probably really enjoy them. A more recent game would be
Scratches, which is kind of the middle man between traditional adventure games and
Amnesia.
Oh and I would also highly recommend checking out if you can grab any of these mods.
Mods for Games - Mod DB