My 97 Elantra won't start. It's a manual transmission and I have to depress the clutch to start it. The battery is fine. Today I kept pressing on the clutch and it finally started.

Clutch plate and pressure plate seem to be too weak to pull the car. Or one of the CV joints is detached from the gear box. To test the clutch plate, park the car on flat surface. Pull the hand brake up, start the car, depress the foot brake pedal, depress the clutch pedal, put the car in 1st gear, press the gas pedal and leave the clutch pedal at once, while keeping the brake pedal depressed.
Follow one of the two following statements:
1. Engine does not shut down and remain start. (Clutch plate, pressure plate and clutch bearing defective - Replace all as a set)
2. Engine shuts down. (Clutch system is OK and does not require any repair).

Is there any fluid on the ground near the transmission? It's possible the clutch actuating cylinder has failed. If it was air in the line you would have noticed it the day you got it back. The master cylinder is on the firewall next to the brake master. You can add fluid if it's low. If it's empty then there may be a loose fitting or the bleeder screw on the actuating cylinder may be loose too.

The axle job should not have caused any problem to develop in the clutch.
I don't see how they could have.
If you can work the slave by hand, it may be a problem with the clutch master cylinder. Maybe the rod from clutch pedal into the master is bent or binding up and won't travel into the master. You could check if master operates easily by taking line off at the slave cylinder (or if not able to remove hose, then open the bleeder valve on slave) and see if your pedal operates now. Use a can to catch fluid if you don't want it to spill on floor. If the pedal still won't move it must be a problem with the master cylinder or the clutch rod.
If the pedal works with line removed, or the bleed valve open, then the release bearing inside the bellhousing must be binding up and not moving forward to engage clutch. (The slave cylinder pushes the clutch fork lever which pushes the release bearing forward on a shaft up against the clutch pressure plate to allow the clutch to operate .If the release bearing is the problem, the transaxle will have to be removed to fix it.
As I said, though, if you can operate the slave and the cllutch lever it pushes with your hand, it doesn't sound like it is binding down there. Check the pedal's push rod going into the master cylinder. Good luck.

Go under the dash and bypass the clutch pedal safety switch and see if it starts.

Looks like a clutch master cylinder or slave cylinder malfunction.

Unfortunately, and I don't like saying this in the least, the problem is going to be the transmission leading to other issues. Your going to have to have the transmission repaired.

THERE ARE MANY POSSIBLE CONDITIONS THAT COULD PREVENT YOURCAR FROM STARTING. 1. NUTERAL SAFETY SWITCH IF THE CAR HAS AN AUTOMATICTRANSMISSION. 2. CLUTCH POSITION SWITCH IF THE CAR HAS A MANUAL TRANSMISSION.3. BRAKE PEDAL SWITCH. MANY NEWER VEHICLES HAVE A SWITCH ON THE BRAKE PEDAL ANDIF THE PEDAL IS NOT DEPRESSED WHILE TRYING TO START THE CAR, THE CAR WON'TSTART. ANOTHER POSSIBLILITY IS THE SECURITY SYSTEM. DOES THE CAR HAVE ASECURITY CHIP IN THE KEY? THESE ARE SOME OF THE MOST COMMON REASONS THAT A CARWON'T START FOR NO APPARENT REASON. HOPE THIS HELPS.

Worn throw out bearing, replace or the problem may damage other components. This requires dropping the entire transmission. this bearing sits between the clutch pressure plate and clutch slave assembly. When the clutch pedal is pressed, the bearing makes contact with the spinning clutch pressure plate. If defective, grinding/squealing noises may be heard. If the bearing fully fails, loose debris may damage other components. Replace immediately!!

try to move the floor mat out from under the clutch pedal and push clutch all the way down. if it starts then adjust clutch switch. if not then a full diagnosis of starter system is required

try pushing the clutch to the floor with you toes if it starts and won't unless you push to the floor its the clutch start switch 22 bucks at auto zone i will be gettng help installing the new one i will let you know.