My desktop crashed!
MY desktop crashed! Am I able to retrieve songs from my library using my iPad?
You might, if they are still in the store (rights-holders can remove their content at any time) and you haven't moved countries since buying them, be able to redownload your iTunes store purchases via the Purchased tab in the iTunes store app on your iPad - and, if you had subscribed to iTunes Match on your computer's iTunes and uploaded it to it, your own music : iTunes Match on iPhone, iPad, or iPod touch - Apple Support.
You haven't got a copy of your iTunes downloads/library on a backup drive ?