Can I use my time capsule for wired Internet?

The basic question is, can I connect my time capsule to my home internet router wirelessly and then use the time capsule to connect my iMac to the Internet with an Ethernet cable?

THe back story: I have a late-2009 iMac i7 that worked beautifully until somewhere around OSX Lion. The update came, and suddenly the wifi became shotty; intermittent connectivity that would last anywhere from 2 hours to 2 minutes, and often times, the computer would abruptly shut down. So, I simply ran an Ethernet cable from my comcast wireless gateway directly to my time capsule and then ran another from the TC to the iMac. This worked wonderfully when the router and the iMac were in the same room. We have since moved and there is only one working coax hookup in the new house, and that room will not accommodate a desktop computer. Now, I have searched high and low for a fix for the wifi issue, to no avail; resetting PRAM, changing the wifi channel, resetting the wireless packages, you name it I've tried it (with the exception of a sketchy-seeming reinstall of pre-lion airport firmware). I really don't have the money to have someone come and run an Ethernet cable through my walls right now or figure out the coax cable situation (I tried to muddle through it myself but there are around 10 outputs and the room I want to use actually seems to be wired directly to an old Hughes-net satellite on the side of the house 😟). So right now, this wireless to Ethernet dream is my only option... Any way I can make it work?