You are running two different networks.. you cannot do that unless you know exactly how to set it up.
The TC has to belong to the existing network otherwise you have dual gateways and everything falls apart.
Plug the TC into the existing router using ethernet to the WAN port.
Press and hold the reset for 10sec to reset.
Connect one computer by ethernet to TC LAN port.
Go to the airport utility manual setup.
Go to internet tab, connection sharing, and select off, bridge mode. Update the TC.
Then you need to do all the setup I previously mentioned.
TC name and wireless names SMB compliant.
Open the guest account on file sharing to read write
Put in the correct workgroup
I then suggest you shut down the whole network and every computer and device.
Start the modem and wait until it boots correctly around 2min.
Start the TC and wait 2min..
Then start all the client computers.. plug them into either main router or the TC.
That will allow you to access the TC on the network without issues.
Your problems are then purely windows.
And for that I left being a computer technician when vista came out.. as it is a heap of smelly substance... and took up Mac. So it is the bugbear of my life that it doesn't just go away.
The TC will work fine with windows.. if you have further issues, get a computer technician.. who can still stand it.