Somehow it looks like the problem is some keyboards sending the wrong "enter" signal. There's a way to rebind it so that it uses the right one.
Install Sharpkeys (
http://www.randyrants.com/2011/12/sharpkeys_35.html). Run it, and click "Add".
Click the left "Type Key" button, then press your "Enter" key. You will see some key ID (when I press my usual Enter button, it appears as "Special: Enter"; when I press the one on my number pad it appears as "Num: Enter"). Click OK on this. Then, on the right-hand side, scroll down until you see "Special: Enter".
Click OK. Your selection will now appear in the main SharpKeys box. Click "Write to Registry", and it will commit the change (don't worry, this is completely reversible)
Click Close, and reboot your machine. Now your Enter key will be seen within Windows as a regular Enter key, and not whatever it was bound as before - and so it should be accepted by Theme Hospital.
If you want to undo this change, just start up SharpKeys again, delete the binding from the list (choose it + Delete, or just Delete All), "Write to Registry" and restart again. This will remove the new keybinding entirely.
Hope this helps!