First thing to try is the latest version of Lightroom (currently 5.6). If it don't crash, then problem solved - upgrade.
If Lr5 won't run on your machine, then Lr4 instead.
If both Lr5 and Lr4 crash on your machine, then at least you know it's a not a Lightroom version problem but something wonked in your system.
If you can't figure out how to resolve the crash on the system you have, then it's time for a new system (or try another converter/editor app).
PS - A few things to try:
* After re-installing new version, if that doesn't fix it, then get rid of all Lightroom-related data files (rename them so they can be restored), in case problem is in Lr data file.
* Remove all non-essential hardware in case problem is hardware/driver.
* Startup up machine with minimal software services.
* If still no go, consider updating driver software, including mainboard drivers and/or bios firmware if need be.
* Of course run all the system hardware and software diagnostics you can - problem could be failing disk or ram..
* Check system event logs for any clues.
If you don't know how to do some of these things - ask.
Do not say "you've tried everything" unless you want a lecture - there is most definitely something you haven't tried. It's like when you can't find your car keys - you haven't looked everywhere - there is somewhere you haven't looked!
PS - Has Lightroom EVER worked on your machine? what's changed since then..