The problem is the management structure leading to internal billing sounding like a good idea! Flat rate the costs unless they're really significant and you can't gauge who the users are. Make the flat rate based on 'reserved' units. i.e. a portion of the resources have 'priority' access for a dept. based on the amount the dept. allocated to the budget. They are still shared, but the sponsoring dept. has priority access. Infrequent users use the 'free' equipment or any 'reserved' unit not currently in use. Frequent users can fund additional 'sponsored' units if they need more. While imperfect, it's better than treating each bit of equipment like a rent-way rental.
The AC's idea of an RFID timeclock in the room is great if you must internally bill. A crude measure of usage should work if your office politics aren't toxic. If you really have problems with equipment abuse, you can use a webcam and review it only if there is unreported damage. Review the footage only with a managers approval with public knowledge every time it happens (with penalties for snooping) and you'll make junior NSA drama less likely.
Still, internal billing is very expensive operationally.