Ubuntu and its derivatives are also live distros you could try.
What hardware is failing? Typically the problem I see most is with video cards. Try Ubuntu. It has worked for all ATI and NVidia cards I've used. There are special kernel modules for each and Ubuntu imports them during install.
It may not be the silver bullet, but of the distros I've used, it seems to be the easiest. Here's a list of what I use/used...
Red Hat 7.3, 8, AS3, AS4
Fedora (several versions)
Cent OS 5
Mandrake (my first distro - 6.1) used it through 10
Ubuntu/Kubuntu/Xubuntu since v5
SuSe (on iSeries)
Knoppix
DSL
FreeBSD (not exactly Linux, but has a similar feel)
Gentoo
Xandros - for about 15 minutes!
There have been others, but these are worth mentioning. The trick is find what you're most comfortable with. Most distros are similar at the core, it's the fluff (GUI tools) that differ. Try 'em all, most are free to download.
Mark