I think it would be very difficult, given the LVM. I've usually just written off the data in that case; it's seemingly part of the tradeoff for the advantages of LVM. But if you were to try, I'd first copy the whole disk using dd from a boot CD. Don't mount it (no automounting), don't touch it, just make a copy first onto another drive. Experiment on the copy. If you remember the exact configuration of the old LVM partitons and volumes, it might just work to rewrite the partition in fstab and remake the LVM exactly as you did before without formatting. Or it might not. There some commercial utilities that might work to find files or directories. I've used R-Studio's tools with some success.
It may not helpful to say it, but unfortunately this is a learning experience: backup early and backup often. Don't run as root routinely and be careful what you type.