Firstly just power on the TC with exactly the same network setup (hardware I mean).. ie plugged into the main modem or router exactly as it was before you pulled it out.. power it up. I see no reason for it not to work.
If you have already done that.. the problem is not, Time Capsule finding the computer.. it is the computer finding the TC.
The method of getting things going again is to apply a factory reset and start over. No files are lost doing this.. you will then run through the setup via the airport utility.
The Factory Reset universal
Unplug your TC/AE. Hold in reset. and power the TC/AE back on.. all without releasing reset and keep holding in for about 10sec. The time is not important.. it is the front LED rapid flashing that indicates you are in factory mode.
Release reset.
If it doesn’t flash rapidly you have released reset at some point and try again.
Be Gentle! Feel the switch click on. It has a positive feel.. add no more pressure after that.
TC/AE will reboot after a couple of minutes with default factory settings and will wipe out previous configurations.
No files are deleted on the hard disk.. No reset of the TC deletes files.. to do that you use erase from the airport utility.