<VV> Transmission help-Reverse

[R. Byers]

I have just completed reinstalling my engine into my 62 Monza, repairing 
things I have known to be wrong as I have gone along, including the brakes, 
U joints, flywheel, clutch and, of course a new engine, replete with new 
center carburetor and linkage.
Much to my chagrin, upon starting it and moving it for the first time under 
its own power, I found first, second, third, and fourth gears... but no 
reverse.  The shifter moves into the correct position for reverse, but.. 
nothing happens.  I have looked and checked and I can find nothing amiss.
My first instinct is to think that I need a new transmission (or a new 
reverse gear), but I thought I would write and ask the experts if there 
might be some adjustment or something I am missing.  I just can't see what 
else it could be from looking at the manuals, but it is depressing after 
coming this far.
Additionally, as this is a modified 140 engine, and assuming it IS a bad 
transmission, should I take the opportunity to get a late model transmission?
Thanks for the help!

Ron Byers
Largo, FL