Well... Wireless is out of the question I think.
Will the building manager let you use existing wire in the building? You could use the existing TP connections that exist in the building if you get permission from the building management and cross connect them in their wiring at the buildings demarc.
I wouldn't expect it to be reliable as a direct ethernet connection, but there are cisco products that can help you use exisiting TP connections.
http://www.cisco.com/univercd/cc/td/doc/product/lre/
Just an idea.