Comcast has gotten a lot better about supporting customer equipment. They maintain a "supported device list" and as long as you buy something off that list they'll help you. Granted if you're buying your own device you should be prepared to do some minimal troubleshooting like using ping and looking at LEDs.
I once came home from a business trip to no internet. When I called Comcast I explained the troubleshooting steps I took and what the modem was reporting. They sent a tech out in 2 days to tone the line. When they couldn't get a good tone they sent a level 2 tech out to replace the line. Turns out someone had put a screw through a cable chase when they were re-siding the building while i was away.
I’ve also never had a problem activating a modem. They ask for the MAC, model number, and sometimes S/N, then it works. The model and S/N are optional and don’t even have to be correct.
They’re a terrible company and I would not deal with them given the choice, but this isn’t one of the reasons why.
In which case you can take your router completely out of the picture by plugging your computer directly in to Comcast's line.
I used to work for Comcast, I have some insight into how modem activation works, and I know the troubles people with their own router go through.