There must be a million questions similar to this on AB (FYI: check before posting)...
The K750i seems to develop this over time.. I have one myself and it drives my crazy sometimes..
Sony won't do much because they put it down to 'wear and tear'.. best bet is to clean the phone, strip it and spray some WD40 (or equivalent) neatly around the joystick..
As for your eBay troubles, that's probably why the seller got rid, however the only thing you can do is tell eBay you received goods 'not as advertised' unless they mentioned in the ad that it had a sticky joystick, then your pretty screwed! eBay may compensate you, but don't hold your hopes too high.
Repairs at a shop.. take it to a Carphone Warehouse, they seem to be authorized repairers of Nokia and Sony etc.. Could cost anywhere from a new keypad to a new phone..