How can I fix a broken cable inside a akg ht400

We do not have parts. Sorry

use another headphones cut them and splice the cables together carefully.

Being a dynamic microphone there is not much that can go wrong with it apart from:

1. 
   broken / detached wiring
2. failed diaphragm capsule

before doing anything else check it isn't a cable fault.
AKG products normally have a 2 year warranty so if it's inside that time take t back for repair / replacement.
Otherwise a competent repairer ought to be able to fix it for you cheaper than replacement

Cable is damaged. Find an old stereo shop repairman or ex-Navy electronics guy to see if they will repair them for you.

One of the coil wires in the diaphragm might be broken. Try testing it with a volt ohm meter.

Have you tried using a another XLR cable..,or are the other mics phantom powered condensers..ie try to locate if its a mic problem or the cable..2 other points are 1 - XLR leads for phantom mics need to be XLR to XLR male to Female plugs[ends] 2- is that often an XLR to XLR cable will be not soldered or wired right,so that the power [phantom power is not getting to the mic] so ensure you have a proper cable for that job...Sorry i can't be more specific but from reading your problem all these issues come to mind..If you have ruled all these things out,then it could be the capsule or loose joint or component in the mic which means contact AKG,pro audio services or find a DIY mic person to help..G luck!!

I am having the same problem on 6 new CHM 21 units myself. Has anyone helped you with this problem?

Those units are on frequencies that the FCC sold off to the cell phone/telco companies a few years back, and are now actually ******* to use in the USA. The reason you are getting all that hash noise is because you are being stepped on by cell signals. Sell it on eBay Mexico or Europe and buy a new rig.

http://www.lenoxx.com/2005/manuals/ht400/HT400manual110502.pdf

take your broken aerial and go to (radio shack)near you and buy a similar one and fix it in your system with screwdriver.