Many thanks for your help.
I tried the 2 tests suggested by the link you provided.
(1)memtest86 v2.11 ran for 4+hours and seemed to show tens of thousands of errors(!) although it also said it passed 15 tests. I'm afraid I don't really know how to read memtest.
(2) I have an old DSL CD (version 3.3) which I assume is the Koppix suggested. After bootup, this seemed to show a window full of errors - for example "I/O error: 0b:01, sector 69300" and same error message with different sector numbers. Koppix finally said "Restoring backup files from /mnt/hda1 mounted on /dev/hda1". But after awhile "Unable to handle kernel NULL pointer dereference at virtual address 00000020".
Is my PC ready for the tip?
If so, is there any way to restore my personal files (email a OpenOffice files)?