Ok a few simple things, when you plug up the cable, do you have any lights on the connector in the computer that might come on?One of them will be the link light, and the other will be the activity light.
One should be steady(the link light) and the other should blink(activity), not a steady blink but when data is being sent in and out of the interface.
Some things to check in windows,
1. Make sure that the network interface is ENABLED, and is not DISABLED.
2. Is this computer on a network using DHCP? If so, go into the TCP/IP settings for this network card and make sure it is setup to use DHCP and doesnt have an address in the fields, if so click on the spot to change the card to DHCP, and make sure it does DHCP for the DNS server settings as well.
If the computer is NOT on a network that uses DHCP, then set the IP address parameters to what is needed for it to work on the network.
3.Make sure to set the interface to 100mbs FULL duplex, Some network cards and switches (esp the cheap ones, which a trendnet is considered a cheap switch) sometimes dont work together for the speed sensing. if the 100 FULL DUPLEX does not work, then try 10mbs and HALF duplex, and see if this works. If it does work for you then, your network card chipset might be bad or it could still be an issue with the switch.
Did the network card work previously in this computer? If so, did you update a driver for it? This could be an issue, if so, roll the driver back to the previous one, this should fix it for you.
If none of this helps, then it is possible that the network card is bad, and will need to be replaced.