if after changing the battery the little red light still doesnt flash, then its the lower remote part which is faulty...
if you purchase a used remote off ebay, you can replace the lower part (the bit with the buttons on it) and attach the top part (the key bit with the all important immobilizer chip and key) from your original key
once you've got a used 'working' remote with which the red light lights up when you press the buttons then you can code it to your car using the method i detailed above or using vcds... the dealer will want to charge you an arm and a leg and spin you the line that you can only replace the entire key and not only the lower portion!
MVB12 - when you change the battery try to be as quick as you can about it! i suggest you have small 'jewellers'/watch flat screwdriver handy to pop the old battery out, i was told by the vw service guy that the remotes have 40seconds within which the battery must be changed otherwise they need recoding...
good luck chaps