I had a system that was banned and I just moved my hdd over to another one I bought on ebay (that wasn't banned but gave me 3rod every now and then) and it works great. No problem with connecting to live at all.
And on a lighter note, I just got off the phone with xbox.com and ask them to fix my xbox 360 (the one I got on ebay for 50 bucks) and they said no problem (it was giving me freezing and 3rod). It cost me 160 bucks but they said I would not get my old system back but a new one instead. (hoping for an elite but doubt it but it doesn't hurt to hope) It also comes with a 1 year warranty (renewable from year to year for 29 bucks a year) to cover my system and controllers. It also comes with a month of live for free (not that big a bonus but something and she said I get something else for free. Was hard to understand her) and of course free shipping there and back. So when you add it all up it cost me 210 bucks for new system with 1 year renewable warranty. Not that bad of a deal considering what it would of cost me to go out and buy a new system, even a core at that.
There are quite a few consoles out there on ebay that are not banned and have the 3rod. Might be an option that people would look at instead of paying full price for a new one.