If the immo chip is in the key, you might indeed have an antenna near the ign. switch. If the chip is one of those littel dangly things on the key ring, you probably don't have one there. Is it the type where you have to physically put the chip into a socket or touch some other contact?
It sounds like, as you sent the parts away, that it is an aftermarket system, is there any marking on it to identify it or the maker?
If it turns out that there IS an antenna where you suspect, it will not be coded in any way (it will be a resonant length wire, which you need not concern yourself about, unless it is broken).
If it is there and can be removed, get a multimeter and check for continuity, but don't bung a load of V or A thru it! There could be an amplifier chip in it somewhere. If open circuit, you may be able to unwind the very fine coil of wire and re solder the break, this is hard and needs much care to avoid shorting the coils to each other. Or carefully remove the coils and count them as you go, get some coated (NOT plastic insulated) copper coil winding wire of the same gauge- used to be shellac'd-maybe from RS components or Maplin and rewind same number of coils back and check for open/short circuit as above.
I did one once on a Renault Espace, and got a result, but it was potentially risky! The likelihood of getting another if you ruin it is not helped unless it can be identified, and may still prove hard if the unit is as old as the vehicle.
Also, make sure that at least 12v is getting to where it needs to; voltage drop can wreak havok on immo's like this. I have seen it so myself! Don't forget to post back on here if you get a result please.