Can a cable modem get infected ?

operating on XP, w/ a Toshiba Satelite series laptop, Time Warner/Road-Runner hi-speed Cable modem service

Accidently clicked on a pop-up, got a trojan horse, in the form of changing my background into a message that I have a virus & to click here for a sacn ...

Well I didn't, I brought it to my local GeekSquad, they did an "Advance Diagnostic & Repair" it cost me $200, they took 3 days to "clean" it told me it was a "bad one", Vidamod or something like that.
2 days later the virus seemed to reappear (changes the background to a red tint & all the desk top icons go "blue square") so I took it in again they did the same service again, no charge, 3 days later it was given a clean bill of health...
Well it's been 2 days & it happen again (red tint, blue squares around desktop icons) I removed the modem cable from the back of my laptop & the background & icons all went right back to normal ... ??? I called GeekSquad about it, they told me it might be the cable modem being infected ... Time-Warner says it's impossable but will give me a new modem, my companie's IT told it impossable also ...
Is GeekSquad just not removing it correctly or what ... Help ???