Have you reset the TC to factory and redone the setup? This is a major fix for a lot of issues. Simple fact is the TC needs a boot in the pants every now and then.
I have unplug the power cord & plug it back in.
That is not a factory reset..
This is a factory reset.
Factory reset universal
Power off the TC.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the TC to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
N.B. None of your files on the hard disk of the TC are deleted.. this simply clears out the router settings of the TC.
How is the TC setup in the network?
not sure what you mean by this, followed the prompts when i set it up.
Open the airport utility when the TC is working.. click on the TC and take a screenshot of the summary info.

Then click edit and go to the network tab.. take a screenshot of that to and post it.
What is the link speed between the computer and the TC??
Please run the wireless diagnostics and then the utility which is part of the diagnostics and tell us or post that as well.
About Wireless Diagnostics - Apple Support

