Is the Mac connecting by ethernet or wifi? I don't see that you have told us that.
Look at the connectivity led for ethernet on the TC if you are using ethernet.. and also look at the TC log.
Is it a Gen 3? Does the log show a whole bunch of events where the TC is connected and then disconnected..
If so your TC is dying. It has nothing to do with any update.
If you are connecting by wireless.. I am not sure.. but it is still probably an indication of the TC on the way out.. if it is an older Gen 1 or Gen 2, then just the standard power supply issue.. but somehow it is the imac affecting it more than anything else.
If you haven't changed anything recently it is hard to imagine how... although upgrade install of Lion is known to mess up the wireless.. usually won't affect the rest of the network.
I would reset the TC and change its name as well as the wireless names to SMB standard.. short, no spaces pure alphanumeric.. I do not run Lion and don't have issues.. (as a consequence).. but I have noted people advise this.
Set a different name for 5ghz.. follow the same rules.
Then do a test.. with no security.. if that works then add wpa2 personal security.. passkey of 8-12 pure alphanumeric characters.
Make sure the country code is set correctly and the Mac is picking that up from the TC.
Look closely at the TC log.. it does show a lot of info.
I've never messed around in Console before. What am I looking for in the logs? Is this evidence of the problem:
7/8/12 9:19:13.118 PM com.apple.usbmuxd: _SendDetachNotification (thread 0x7fff767cc960): sending detach for device d0:23:db:af:0c:b8@fe80::d223:dbff:feaf:cb8._apple-mobdev._tcp.local.: _BrowseReplyReceivedCallback got bonjour removal.
Well, that was a challenge, finding my TC log -- since AirPort Utility 6.1 doesn't include logs and 5.6.1 doesn't load on OS 10.7.4. Eventually I got to 5.6, and what I saw on the log didn't point out any obvious problem.
Here's the entire log from the time I turned on my offending Mac to the time I turned it off, including when the internet disconnected and briefly reconnected, as viewed from another Mac that doesn't cause problems for my Time Capsule.
Jul 09 22:36:48 Severity:5 Associated with station d8:30:62:5d:b7:0b Jul 09 22:36:48 Severity:5 Installed unicast CCMP key for supplicant d8:30:62:5d:b7:0b Jul 09 22:36:51 Severity:5 Binding added for udp, 192.168.1.33:32771 to 10.0.1.3:5353 with lifetime 7200 Jul 09 22:36:54 Severity:5 Connection accepted from [fe80::da30:62ff:fe5d:b70b%bridge0]:49152. Jul 09 22:36:54 Severity:5 Connection accepted from [fe80::da30:62ff:fe5d:b70b%bridge0]:49153. Jul 09 22:36:55 Severity:5 Connection accepted from [fe80::da30:62ff:fe5d:b70b%bridge0]:49154. Jul 09 22:39:53 Severity:5 Connection accepted from [fe80::60c:ceff:fed8:5da4%bridge0]:50375. Jul 09 22:39:54 Severity:5 Connection accepted from [fe80::60c:ceff:fed8:5da4%bridge0]:50376. Jul 09 22:40:06 Severity:5 Connection accepted from [fe80::60c:ceff:fed8:5da4%bridge0]:50377. Jul 09 22:40:07 Severity:5 Connection accepted from [fe80::60c:ceff:fed8:5da4%bridge0]:50378. Jul 09 22:40:07 Severity:5 Connection accepted from [fe80::60c:ceff:fed8:5da4%bridge0]:50379. Jul 09 22:43:27 Severity:5 Binding dropped for udp to 10.0.1.3:5353 Jul 09 22:43:31 Severity:5 Disassociated with station d8:30:62:5d:b7:0b Jul 09 22:43:31 Severity:5 Rotated CCMP group key.
Nothing jumped out at me as wrong, but I don't especially know what to look for. Is this helpful to you?
On your computer, open System Preferences and navigate to Network. From the top of this pane, create a new Location name (such as today's date or other preferred name). Make sure you click Apply, on bottom right.
You may also consider changing your network channel to either 3 or 9.
If all else fails, I suggest downgrading the firmware of the Time Capsule.
Airport Utility 6:
Open Airport Utility and select the Time Capsule, hold the Option key and single click on the Version number. Choose 7.5.1 if available.