I'm working on a Trek 4100 and just received a fork that I need to put on the bike supposedly from another Trek 4100. The shaft coming off the fork is not long enough to reach out of the front yoke to receive my handlebars ??? My question is it possible to take the shaft off the original fork and put it on the newer one ? Do I need a press or is it screwed in to the fork.

That "shaft coming off the fork" is called the steerer tube. They're typically cut so that they'll extend up out of the frame's head tube just far enough to accept the headset and stem, plus maybe a few spacers. It sounds like the fork you received was cut to fit a smaller frame than the one you're trying to install it into. Unfortunately for you in this case, steerer tubes generally aren't swappable. They're an integral part of the fork and not meant to be removed and refitted.

I did once have the steerer tube come off the fork due to a crack while riding and a frame builder was able to repair the fork by brazing in a new steerer tube (some repairs to the head tube were also needed where it hit the pavement). But I agree that they are not designed to be routinely replaceable.

You need a different fork. Frames come in different sizes and it's obvious the fork you have was for a smaller frame, despite being from the same model and make of bike. There is no reasonable way to make the new fork fit your frame.

**** then, Anyone have a fork that has a 9-3/4" steering Tube. I got this set and handlebars for free from CL.

threaded or threadless 1" or 9/8"

How shy of what you need is the steerer?

9 times outta 10 you're better off getting a fork with a longer steerer.

If you can find someone with the old style Spank Spike stem, that'll do if you're only short 10-15mm. Finding one might me nigh on impossible, though. They stopped making those over 5 years ago.

Sounds like threadless to me. I think all 4100 were 1-1/8", I'll check real quick, though.

Yep, all threadless 1-1/8"

I have faked short steerers with a Steel tube type quill stem raiser..
The one with a 1" OD on the bottom will work.

crank the quill wedge tight , then up top, put the star nut in. Upper OD is about 9/8".

NL's BBB's BHP 21 is a more sophisticated Piece . they had a Quill bolt custom manufactured for them
(in Taiwan of course) it is internally threaded 6mm inside the 6mm hex used to tighten the wedge.
to be a part of the piece.

Hmmm. So you have 2 similar forks, neither of which is usable? That means you have nothing to lose.

If it was my bike I'd disassemble both forks and see if I could mix and match the pieces to make one fork that met my requirements.

Ok looked up what a 4100 was..

Just buy a new MTB Suspension Fork . or a rigid one made to replace suspension forks .

or, agree with RG, overhaul both and mix and match
the stanchion/blade tubes & steerer fork crown assembly.

as you should know, the suspension comes apart from the bolts on the bottom ends
of the cast lower portion.

If that is news , you may want to delegate the work to a Shop.