Have you updated Parallels?
Have you updated Parallels to the latest version?
The latest version is 4.0.3846 as of this posting. You must have this version to support OS/X Snow Leopard as a Host Operating System. All earlier versions will not run and crash immediately.
I am not sure from your post if this is the issue or not. It is good that you backed up, but I would suggest upgrading from version x to y in the future first. Only then would I attempt upgrading the operating system.
I hope that an upgrade corrects your issue it that was the problem.