hi there: looks like a pretty confusing issue for you. you mention that your laptop works on your WiFi LAN, but you don't mention how your LAN is configured, your wireless Router/Gateway device make and model or anything. pretty hard to troubleshoot your problem without that. you mention you built your pc, did you build your LAN as well, or did someone else in your household do that? you also mention that your laptop connects to the internet through your LAN on WiFi, but not on a wired connection *using an ethernet cable*. Have you tried connecting your laptop to a friends' LAN using a wired connection? If that doesn't work, your built-in LAN port *ethernet* port could be broken on your laptop or simply disabled. If the hardware is broken, it will never work on your HOME LAN in wired-mode. If it's simply disabled, you may be able to resolve by making sure the internal LAN function is enabled in your laptop's BIOS setup program. Also, have you tried turning off your wireless switch on your laptop when you try to make a wired-connection through your wireless router? Having your wireless LAN enabled on your laptop at the SAME TIME as trying to connect via a wired-connection causes conflict in many laptops--you can run on or the other but not both together.
Let me know what your router make/model is, and I'll try to help if my other suggestions don't resolve it. Also, have you tried calling the Tech Support line of the router manufacturer? If it's less than 1 year old, most of the major companies will give you free tech support on installation issues for the first year.
If you didn't install the LAN but someone else in your household did this, ask them for help. Also, ask them to log into the router and check the internal settings. If you installed the LAN, then you should be able to check the router settings yourself. If you cannot do this, and you can't get through to the manufacturer's tech support, replace the router, it's probably bad *especially if you got it used and didn't buy it new*.
Luck.
BIGBEARJEDI.