Since the computers are on a workgroup, even if you have the exact same account named Administrator, using the exact same password, these are still two seperate accounts, and MAY be part of the problem. This being said, try this...
As example, say the desktop is named "desktop", and the laptop is named "laptop". The Administrator account(s) (or any accounts) would be as follows:
If on the desktop, using the permissions on the shared resources, gave full control to user: laptop\Administrator then that user "should" have full control. This may be just another "feeble" attempt, but it's worth a shot. Let me know how it goes.