I have a KLH21 serial # 01237, so it is near the beginning of the run.
makes noise like a radio, hiss and all that, but will not tune a FM station.

I checked all the antenna connections and that all looks good.
I would like to get it repaired.......

Take a look at the following:

http://antiqueradio.org/KLHModelTwentyOne21FMRadio.htm

Also, dig around on http://fmtunerinfo.com

As suggested on the article on the antiqueradio site, a fairly common
problem in older FM radios/tuners is that they develop bad contacts in
the air-variable tuning capacitors. The metal shaft of the capacitor
(which is connected to the tuning knob, and to the movable "vanes")
is normally connected to ground via some sliding contacts - metal
"fingers" located where the shaft goes through the metal body of the
capacitor. The "fingers" are connected to the metal body, and are
supposed to rub against the moving shaft and make a good electrical
contact.

Over the years it's common for dirt, dust, dried-out lubricant (oil or
grease), and oxidation to build up on the ground fingers and the end
of the shaft. This gunk interrupts the electrical contact, and the
"tuning" of the radio becomes scratchy, noisy, irregular, or
completely unstable.

This may be what has happened to your KLH.

The fix for this is fairly straightforward - flush out the gunk,
restore good contact, and lubricate. A lot of people swear by Caig
Labs "DeOxIt" spray for this... the D-5 spray is about 5% of their
cleaning material mixed with a solvent. Note - do not "go crazy" and
spray this stuff all around the tuning capacitor - you do *not* want a
residue of this on the plates or vanes, as it will de-tune the
capacitor and possibly make things worse. Instead, carefully spray a
small amount of it into a small dish or bottle cap, then transfer a
few drops of the liquid to each contact point on the capacitor shaft.
Rotate the cap through its full tuning range a dozen times or so,
allowing the DeOxIt to break up and dissolve the accumulated gunk and
oxide.

That may be enough to restore your radio to usability.

I personally prefer to use DeOxIt to restore the contact, then flush
it out of the capacitor entirely with a "no residue" contact cleaner,
then add a drop of a lubricant such as FaderLube. Other people think
this is unnecessarily-complex overkill.

If cleaning the tuning cap contacts doesn't restore the radio to life,
and you can't find any broken wires, then you'll need to take it to a
technician who has the experience and equipment to do a repair and
re-alignment. The fmtunerinfo site has leads to some shops which
still have the necessary skills.