First off, welcome to the forum JTD1688!
Now, you said you lose connection if your computer is not on or on standby? Well simply try unplugging the computer from the router and a power cycle of the modem and the router. Comcast is know to have problems with the Xbox Live service. So can you do a few things for me? Do a Dual Speedtest, select server1. Once done post the results here. Next, on your computer do this. Start> Run> cmd> tracert testmy.net Once this is done copy and paste our results. If none of this seems to work then a simple call to Comcast would be great. Thanks, and again welcome!