Befriend your local IT expert and get them to give you Admin rights on your computer.
Not come across webmarshall, is it some sort of firewall/pop-up/adware blocker software ?
Probably the easiest option if you've got Firefox on USB (presumably using
Portable Apps?) would be to take the USB disc to a computer where there are no restrictions (e.g. home) install there, then take the USB drive back to work the next day with
Zotero installed.
P.S. - Clicky links to pages about software that people may not know about is useful/appreciated