Eddy, MikeBCda, thank you both. I have now re-installed Windows and the computer seems to be working fine: no hangs, blue screens or anything of the like, so I assume it must have been some software conflict causing the problems. This time I proceeded vey cautiously and step by step, which is why I took so long to reply.
Eddy: with regard to the memory test, I counted 13 passes before aborting, which is a rather good result, isn't it?
I've now connected to the Internet wirelessly but have been having problems updating avast. Each time I try to update I get a message saying:
Error when updating avast! Last encountered error: Other HTTP error (302) while trying 67.15.0.83:80/iavs4x/servers.def
Any ideas?