Thanks Geoff, sorry for the delay but have been super-occupied. The machine in question is a Compaq Presario V6216EA so it's not too similar to your big Dell. Getting to the memory isn't, I think, too difficult though so I'll add that to my not very long list of things to try.
I think that this machine is at RAM max with 2Gb. Since one explanation of the freezing given to me was that it was due to a dying HDD, I've been trying to find out how big a drive can be recognised and used in this machine. Some reports say 200Gb, others say 320 Gb. One article even said 500 Gb or more but I'm not too convinced by that advice. In any event changing it might be a very cheap fix (or, perhaps, not) and doubling the disk capacity would give it a new lease of life. I wish that I could find an authoritative source of information because there are so many versions of this computer.