It might be that only a basic TCP/IP stack is loaded in networking + safe mode, in which case only the wired network will work, also you may go in to command prompt C:/ and type in ipconfig/all, that should give you the details of all the ip addresses and the gataway, if there is no router ip or gateway than you wont have any connectivity.
Also only FTP and UDP protocols may work.
Try pinging an ip address....