Michigan -- don't pitch that RX out just yet.
With regard to your question, Ace is simply incorrect. The antenna wire on the Orange 4 channel receiver is nothing special. It is a 29 mm long piece of standard stranded hookup wire. Probably 24 or 22 gauge.
It's incorrect to state that "most 2.4 systems have a more complicated antenna wire, where only a portion near the end is the antenna".
That may be true for Airtronics, Futaba, and some of the Spektrum receivers (those built for carbon fiber sailplane fuselages), but it's not true in your case, or in the case of many of the Spektrum and JR receivers that have the short "whisker" style antenna systems.
The longer antenna systems that ACE refers to are nothing more than coaxial wire, where the last 29 mm of the coaxial cable's outer shield braid has been removed to expose the inner conductor as the antenna.
Go find an appropriate piece of hookup wire, and solder a 29 mm length onto the pad of the RX where the old one used to be. Go fly and enjoy.
* Making the World Better -- One Helicopter at a time! *