I just created a new user on my Windows XP box, and gave it "Restricted User" access. (I think this is pretty minimal privileges.)
After logging in as this new user, I could use the serial port just fine. I used the 34401A instrument driver to talk to my 34401A DMM and take a measurement.
I think my security setup is pretty standard configuration from Microsoft. Perhaps your organization has imposed even stricter privileges. I searched on Microsoft's web site, and didn't find a lot of information, which indicates that this may not be a common problem.
There are individual privileges you can set (Control Panel -> Administrative Tools -> Local Security Policy) on whether users can "load and unload device drivers", but I think they're talking about
plug and play devices and the actual installation of the drivers. This might apply to you if you are using a USB device to add serial and parallel hardware to your computer. Mine is set to "Administrators" only, and I didn't have any problems with my restricted user accessing the port.
Finally, I'm a little puzzled by your comment that you can't "access all the menus". Do you mean that you really can't see all the menus, or just that not everything on the menus appears to work?
Brian