Router
How is you computer connecting to the internet? From the sounds of it, it's going directly from the wall, to the modem, to your computer. Is that the case?
If it is - you're going to need either a router (either wireless or wired). If you go the 'wired' version then all you need to do connect an ethernet cable from your PS3 to your router. If you go wireless then as long as everything is good to go then your PS3 should find the signal.
I realize this is pretty general so if you need more technical information just let me know!!
Cheers!