Replace one version of Linux with another?

Hi,

I'm a bit of a Linux newbie and would appreciate some help.

I have an old (10 years!) computer on which I installed Corel Linux. It
seems to run fine, but X crashes every time I attempt to Log out -
after an attempted Logout the computer is complete frozen - even
Ctrl+Alt+Del does nothing. The only option is to press the restart
button. I don't know enough about Linux to fix this problem, and I
guess that since the computer is so old it's not likely that there is a
solution.

Anyhow, I'd like to replace Corel Linux with something else like Damn
Small Linux, or similar as I'd like to put it to some use..

Do I need to do a complete re-install with a HDD format? How would a
Linux expert approach this?

Thanks

.