Yes, many do what you want to do.
I would ring AOL and ask them to send you out a free wireless router as they are to new customers who sign up for their £15pm standard broadband.
See if they will also send you a free wireless adapter for your laptop, or if not buy one.
Find out if the desktop has an ethernet port in which case you can just wire it to a wireless router. If not you will need an ethernet card to install.
How technical are you ?