Will not shift out of 1st gear, auto trans - 2002 Hyundai Accent

SOURCE: auto trans won't go into gears

It's highly likely that the shift synchronizer from 2nd to 3rd is worn out. Since most automatic 3 speed transmissions spend most of their time shifting from 2nd to 3rd those synchros are usually the first to go. In most older vehicles I would recommend checking the transmission vacuum modulator, but as far as I know the '98 cherokee does not have one. It is, however, a slim possibility. Check under your vehicle along both sides of the transmission for a small canister with a vacuum line connected to it, or for a vacuum line in general connecting to any part of the transmission near the shift actuator or the tailshaft. If this is present, you have a modulator and it may be bad which will cause delayed shifts, jerky shifting and sometimes no shifting at all into higher gears unless you are at dangerously high engine RPM. If there is no vacuum modulator, you might want to check the wires on the electronic shift control which should be present. Any signs of broken or corroded wires or contacts might be a clue to the problem. If possible, disconnect the wiring harness, inspect it for dirt and/or corrosion and clean it up. Once cleaned reconnect and try again. It is rare for the electronic shift controls to go bad, but it does happen from time to time. Also, does your transmission make a whirring or humming noise when backing up? Especially a noise that gets louder if you go faster in reverse? If so this is a definite sign of serious wear in the transmission and points more strongly to the synchros simply being too worn to allow the vehicle to shift. Let me know what you find out and how it goes.

SOURCE: won't shift out of 1st gear

Replace the output speed sensor on the front of the tranny. It has two wires going to it. ANd looks like a round plug with a bolt like base on it. It is also white.

SOURCE: 1996 Saturn auto trans will not shift into 4th

Check your transmission fluid. If it is bright almost pinkish-red then it is not the transmission. If it is dark red or brown then you need to either get a flush done or replace your transmission depending on the severity.

SOURCE: 88 toyota supra auto trans slips. won't up shift to 2nd gear

yep, sounds like your transmissions on its last leg, mabye you can get by, by starting in 2nd, if you have the option lol, but auto tran's are pretty cheap on ebay or try www.supraforums.com seen one for 300$

SOURCE: 1997 ODYSSEY AUTO TRANS SHIFTS HARD BETWEEN 1st & 2nd, 2nd & 3rd

It has nothing to do with the transmission, it's your engine mount thats bad.