Hello Sam,
OK! a couple of things here to comment on, No.1 Wireless internet access is all good and well if your setup provides a strong and stable radio signal between the WiFi router & PC WiFi adapter. Otherwise I have found wireless can be flakey as hell and full of dropped connections.
No.2 I don't know how familiar you are with traditional wired eithernet type networking, but inorder to use Ethernet (wired) connections with a wireless router over ADSL you must ensure your router is configured to use either "bridging mode" or ethernet enabled or network address translation.
**bear in mind that if you have wireless & ethernet they are seen as x2 different networks or network types, meaning the data packets are of different sizes and therefore might require translation.
No.3 You could try turning OFF the wireless aspect of the device and therefore just use your router as a more traditional wired router i.e. ethernet only.
No.4 YES! you should have your CAT 5 UTP or STP cable checked to make sure you don't have any wiring faults with the actual cable or with the RJ45 connectors.
No.5 Check in windows networking that you have configured the NIC (network interface connector) with the correct components, you should have a) client for Microsoft Networks, b) Internet Protocol (TCP/IP) *uncheck file & print sharing though.
**Essentially Ethernet is using TCP/IP over the public internet & telephone line, ontop of or as part of ADSL.
Ivan