So you've got a Mk4 GTI? We've all been giving you information re Mk5, just as well it was similar..else this thread would have got even more confusing. Correction apparently MK5's WERE around in 04, sorry...cant believe I didnt know that...d'Oh!
If I were you I would look up a vw specialist in your area, take it to them when they are not busy and drop in and ask if they have a look at it, it may not be as expensive as you think.
My local vw specialist fixed my Cruise control for free, that involved hooking up vagcom and making some changes, it only took 5 mins...As a result I now take my business there....(but thats a different story).
I asked the year to see if you were in warranty, you are not, so try to avoid the stealerships and go vw specialist. I am sure if you tell people where you are someone will recommend a place or two.
Probably something just needs reset....dunno if theres a fuse for the central locking, but the fact that your boot opens tells me that the chances are that its not that. Maybe theres someone local with vag com on here who could hook it up and have a look.
Good luck let us know how you get on.