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If you cannot easily run an ethernet cable you'll have two alternatives.
1) Wireless (either add a wireless access point to your existing router and wirless card to your remote computer, or replace the router with a wireless version (most still have wired ports as well for your existing PCs), and wireless card for your PC.
2) Network via the power wiring circuits: Homeplug. There is a thread on it here:
http://www.cableforum.co.uk/board/sh...ad.php?t=35314