Sounds like a hard drive failure to me since an OS install can really stress an old hard drive. If you feel these steps are beyond your comfort or skill level, then take the laptop to an Apple Store or an Apple Authorized Service Provider to be examined to confirm the source of the problem. While this laptop is considered Obsolete (or is it Vintage?) you may not be able to have it repaired by an Apple store, but an independent AASP may be willing to repair and/or upgrade the drive and memory for you. If the hard drive is failing as I suspect, then replacing it with an SSD would provide a nice performance boost giving the laptop some new life.
Edit: I should add that checking the health of the hard drive as I described earlier by using a Knoppix USB drive isn't that difficult (hardest part may be creating the bootable USB drive). As for replacing or upgrading a hard drive, it is very easy to do on this particular model.