Does this mean that you have remote central locking, but only ever had 1 remote key, and 1 non-remote key, and you have lost the remote key?
The alarm shouldn't go off even with the non-remote key, as long as you turn the ignition on soon enough after opening the door (I think you get about 30 seconds).
VW will sell you a new remote key and code it for you, for about £100 I think (phone Peter Cooper and ask them).
You could buy a used remote (usually about £20 off ebay), but you would need to get the right part number for your car as the protocols and radio frequency were not the same for all mkivs. If you still have one remote then it's easy to snap it open and check what part number you need, however if you don't then you might as well pop down Peter Cooper anyway and ask them nicely to look it up for you, then make a note of it yourself.
Once you have a new/used remote key, there are three parts to making a new key match your car:
(1) Getting a blade cut for it (many locksmiths can do this, not just VW)
(2) Matching the remote to your central locking and alarm. You can do this easily yourself if you already have two working keys, using the instructions in your car's manual, otherwise you need special software+cables, which are widely available, not just restricted to VW dealers.
(3) Matching the 'chip' (RFID coil) inside the fob to the car's immobiliser.
(a) If you have the 'SKC' (4 or 7 digit code on a tag somewhere) for your car then you can pay an independent to program the immobiliser on the cheap, not just VW.
(b) If you don't have the SKC then you need to go to VW and their computers can program the immobiliser without the SKC.
If I remember correctly, yours is a fairly early mkiv, so it may have the earlier 'immo2' type immobiliser transponder chips in the fob, meaning that even if you buy a compatible used fob off ebay, the transponder chip can be reprogrammed. For later 'immo3' cars, each transponder chip can only be programmed once, which is why VW will also insist that you buy a brand new key from them, even this is not neccesary for earlier cars; if you take a used immo3 key to VW, they will be able to get you a new blade cut and code it to your alarm/locking, but even they won't be able to match it to your immobiliser, you'll have to pay for a new chip-section of the fob, eg this
There is an exception to 3(b) which doesnt involve paying VW, but it involves finding a car tech guru with special tools who can read the hex code in your car's cluster, and extract the SKC from it, in order to then use with the other special tools in 3(a). I am assuming that you know no such people, and even if you do, they don't owe you a favour.
An alternative to (a) and (b) is to carefully remove the chip from your old key (it will be hidden somewhere inside), and insert it into the 'new' ebay one. However, if this is your only remaining key, and you break it, then you're shafted.