deleted usr/lib/libxml2.2.dylib -- computer won't start

deleted usr/lib/libxml2.2.dylib -- computer won't start

Short version:
I mistakenly deleted usr/lib/libxml2.2.dylib. The computer will no longer
start (just stays in startup mode indefinitely). Would the solution be to
reinstall the operating system? The computer came with Snow Leopard and
have since upgraded to Mountain Lion. If I reinstall the Snow Leopard
version (given that's the one I have a disk for)? And am I in danger of
losing anything on the hard drive?
Longer version: I actually have the correct version of libxml2.2.dylib
saved on the desktop, so if I could get into the computer I may be able to
fix the problem.