93rev2sev showed me a trick on mine. I had noticed that my 1st gear was hard to get into sometimes. I asked him about it and what I learned out of it was shift into 2nd then 1st, and everytime I do that, it goes into 1st with no issues at all. I thought I was going to have to change my fluid, but mine shifted fine otherwise, still does.
I don't mean to disagree with you, but it should go in w/o issues, my 94 does. Also it's not just 1st gear, its all the gears, none of them go in smooth.
Allow me to explain. This may help the OP, too. If you ever have trouble getting into 1st gear from neutral, WHILE STOPPED, then the gears may simply be lined up "off tooth" (were really talking about the synchro teeth and not the actual gears). If gear A is stopped and gear B is stopped, then there is a chance that they are not stopped in the meshed position. Furthermore, there is a smaller chance that they will not mesh when pressed together(they are cut so that this isn't supposed to happen, but with normal wear, it certainly can).
Symptoms:
This condition is noted when you are at a dead stop AND you've had your foot on the clutch (which you shouldn't do) allowing the input shaft to come to a stop. Pushing the shifter towards 1st gear may not make the gear(synchro) rotate at all, which would line up the teeth and allow easy egagement.
Workarounds:
1. Let out the clutch while in neutral and try again. Don't let the input shaft come to a stop.
2. Stick it in second and go back to first gear. There is no chance that 2nd gear is going to have the same problem, and engaging 2nd gear WILL make the synchro rotate, even if it's only 1 or 2 degrees. First will now work.
3. Don't sit at a light with your clutch pressed, in neutral. It's bad on the TOB, the fingers, the cable, the quadrant...you name it.
Exacerbators (compoundable):
Any wear on the synchros
New fluid (increases friction between the synchro and the shaft)
Bearing wear (creates runout)
Worn clutch (easier to disengage, faster to stop input shaft)
In this case, "compoundable" means that with multiple exacerbators, the likelyhood that you can land with both cogs lined up in first gear increases, as does the likelyhood that pushing the shifter towards first will not rotate the synchro enough to allow engagement.
I didn't just come up with this out of the blue.
How it helps the OP:
Chances are not good that this is your problem. Because you've stated that it's better with the car off and the clutch pressed, I'd say a fluid change may help you...quite a bit. With the car off, it SHOULD be notchy. When the input shaft is SPINNING, it should be SMOOTHER. A drain plug or fluid sucker will help you get it all out. I'd use run of the mill dyno-ATF (mercon, not mercon V) and go from there.