There is this Wireless ADSL Gateway/Modem at work (Linksys WAG54GS), I was wondering if someone at work, or system engineer here can be able to see the visited website URLs?
If the router is set up to keep very detailed logs, you might get the IP addresses to which connections were made. I wouldn't count on it, that is a extremely paranoid configuration. It is possible to intercept traffic and thus reconstruct web browsing history.
Your best bet is to look at the machine, web browsers keep history and cache last sites visited.