AFAIK you really need a Mac to mount the Time Machine Disk.
But you may be lucky: Do you know how your Time Machine Disk was formatted? Fat32? HFS+?
If it's Fat32 i think TM created a so called sparsebundle (some kind of growing disk image) that can only be opened with a Mac (Or OS X installed in Virtual Box...).
If it's HFS+ i think TM uses the Disk without creating a Disk Image. But i'm not sure.
You should try to access your disk and tell us what you can see there. If there's a .sparsebundle file/folder you are SOOL. Otherwise (if you can't access the disk at all) you may try to install some HFS+ driver or tool to access you backups.
Then it's just a matter of copying and converting the Addressbook entries.
... For which you may need a mac...?
I think TM can operate on Fat32 Volumes by creating a sparse bundle. It's a disk image scattered over multiple file (avoiding the file size limit of Fat32). But please correct me if i'm wrong. – lajuette – 2010-08-17T11:22:26.293