Later aluminum G4 PowerBooks would put out the dual-link DVI required to get full 2560 x 1600 resolution that 30-inch Cinema Display is capable of, and your big cinema display would plug right in, and work at full resolution. It also uses the full-size DVI connector, built-in to the PowerBook...
The PC laptop may not provide the dual-link DVI, even with the correct adapter. The dual-link DVI uses all the wires in a full-size DVI connector, and a mini DVI connection may not be able to provide all the wires needed for the dual-link DVI.
You would need to check with the specs on your PC laptop. If the video card will provide dual-link DVI, then maybe all you need is the right adapter.
So, the answer is - Yes, you can connect your 30-inch display to the PC laptop, but if there's no dual-link connection, you will be limited to (likely) 1920 x 1280, or something close to that. It won't be as sharp as you might like.