Some more information.
I deleted the VM from the desktop computer (first by removing it from VmWare's library and then physically deleting the files from the HDD), then copied the VM from the notebook.
The results are the same: on the notebook the VM works fine, on the desktop once I press "play", VmWare brings up a black window that stays black and marks the VM as busy, not allowing any action with it.
I turned off the desktop, and physically deleted the VM from the disk through VmWare. VmWare removed the VM from the library but the files are still on the harddrive, and if I try to delete it through Windows' shell, I get that files are in use by a program.
So I guess VmWare isn't able to correctly lock/unlock files? I'm running it in an admin account, and this never happened.
I'm going to answer my own question: no, it's not due to a different CPU but me putting some applications to full screen in the VM. I did just that on the notebook and magiclly the VM no longer boots. So another problem completely.