Random disconnects with my router

Long story short, the sync light on my modem stays on despite being unable to access the internet. According to those "helpful" techs at comcast, this means that the router is the problem.

I randomly get disconnected every few hours on my wired connection. The router is a Linksys E4200. I have tried power-cycling, resetting the router, etc. to no avail. I've tried changing channels and everything (not that it should matter since I don't use the wireless). The modem is this POS that comcast provides me: http://www.amazon.com/Ambit-U10CO1 [...] 001R5DJ7I.

I had this problem in the past, but I was able to fix the problem whenever a tech support person told me to power-cycle the router (I think that's what I done at least). Something about the router blocking the modem.

What should I do at this point?