Assuming the VM uses an NTFS file system, I can't really tell you why you get the error with mapping the virtual disk. What you can try is to map the different snapshots (in the below mentioned order) to see whether one or the other works, and allows you to access the files you need. The current snapshot chain looks like this:
12 - 11 - 10 - 07 - 08 - 09 - 06 - 05 - 03 - 04 - 01 - 02 - base
According to the files' time stamps, the first snapshot was created in August 2013. Don't you have any backups of the VM's files? With the base virtual disk's files it should be possible to recover everything from the snapshots without data loss.
If nothing else helps, you may need to attach the virtual disk (using the latest snapshot file) to a "helper" VM as a secondary virtual disk, and run a data recovery tool to see whether this will be able to detect and recover the files you need.
André
PS: I assume you backed up all the current files to ensure things don't become worse!