My 2001 Elantra did not have ABS.
But still had a tone ring on the right front CV axle.
Looked for wires and found the sensor.
Apparently, it had two vehicle speed sensors
One in the tranny and one on the right front CV axle.
The ECU uses both to determine if engine and tranny are working properly
Otherwise it goes into limp home mode.

You may just need to check the wiring is ok??

 

I noticed you stated you replaced the reg lamps with LED's. Did the problem appear after you did that?
Some Hyundai vehicles use LED's there, but unless they were original equip ,they could cause some problems.

 

I'll check the right/front wheel again but the only thing I noticed was the brake line. I replaced the LED's in the instrument cluster last year and there were no problems. The P0501 occurred early this month when I got the P0734. Actually it's kind of weird how the speedo problem occurred. My overdrive bearing blew causing limp mode and the P0734. The car would shift fine every time I restarted but the limp mode would occur when I would hit around 40 mph. Mind you the speedo and odometer still was working. I took the car out for several test drives and the results would come back the same, limp mode. So I was in my driveway staring into the engine bay trying to figure out this problem and decided to take the VSS out. After that the speedo and odo. was inop but I've taken that out several times before when changing out the starter and everything worked.

 

In the process of replacing the bearing, could the speedo drive gear have moved so it doesn't move the VSS ?

Even if you are getting a reading on the signal wire , that reading should change frequency depending on speed. That would be pretty difficult to measure with a std voltmeter. You would need one that provides frequency readings. That would be my suggestion to confirm if the signal is varying when speed changes. If it is while tapping into that wire it would confirm everything is good coming off the trans. If not, then you might have to open it up and find out why..

 

Just re-read everything, sounds like something went wrong when removing the VSS sensor or repairing the other gear
Who knows for sure?
It is all guess work until it gets fixed

 

Thank you for everyone's help! Let me start by saying that I'm a dumbass lol. So I checked the wiring from the VSS to the harness and didn't notice any breaks or damage. I hooked up the BlueDriver scanner and enabled the MPH on the Live data. I connected the VSS to the harness but removed it from the gear sleeve. I spun the inside portion of the VSS and the MPH jumped up! I spun the gear inside the sleeve which is still installed on top of the tranny and the gear spun freely. So my dumbass did not seat the gear correctly. I took it out and reinstalled carefully until I was not able to spin the gear inside the transmission. Spun the VSS on the sleeve, connected the VSS to the harness and went for a test drive, now Speedo + Odometer works!! Thanks again for your responses!