I have a wired network in my house. I want to add wireless capability while keeping the wired network. Is it possible to simply plug an ethernet cable from the wired router into the wireless router (runs off my PC) to get the wireless network running? Anyone see problems with this?

Right idea.
Best (normal) way of doing this would be to put a wireless access point connected to your broadband router.

You can run the wireless router two different ways.

1) plug the ethernet cable from the wired router into the wan port of the wireless router.
This will cause the wireless devices to be on a separate network from the wired devices.

2) plug the ethernet cable from the wired router into a lan port of the wireless router.
This will cause your wireless router to act as an access point and all wireless devices will be on the same network as the wired devices. Most routers should support this.

Remember to always use secure networks. No WEP as it's less secure than WPA. Be sure both routers have different IP Addresses. If they're from the same manufacturer they may have the same default address and conflict with each other.

Consult your manual and you should find what you're looking for.

Hope this helps.

Using an old router as a DIY wireless Access Point - Setting up the old wireless router :: TweakTown USA Edition