Thanks for the help! Adjusting some settings did it.

I have no idea why the policy was different on this machine, but I compared the two to find out where the differences existed. The most important one (I figure) was:

Computer Configuration -> Windows Settings -> Security Settings -> Local Policies -> user rights assignment > DENY ACCESS TO THIS COMPUTER FROM THE NETWORK

The "guest" was included on the problem machine as a value. I removed that plus I set ACCOUNTS: GUEST ACCOUNT STATUS to "Enabled" in the other part and all is working.

Curiously, the enabled status for the guest account here in the policy settings seems to have nothing to do with the setting of the similar name in the Users control panel. That one is still set to Disabled.

I very much dislike Windows networking and policy rights. It just seems like years of design and feature alteration by hundreds of people not communicating with each other. In the end you're left with a very difficult to manage mess.