My 1999 Hyundai Tiburon will not shift into 3rd and 4th Gear. Is it The Cable? on 1999 Hyundai Tiburon

I have gears 1, 2, 5, and reverse. When shifting into 3rd and 4th the shifter just flops back and 4th. I followed the 2 cables to the transmission, and if I push down on the piece that they are tied into and move around it falls back into place. then it feels like it is locked into 3rd. Do you think it is the cable? Linkage adjustment? Thank you for your help. It needs to last a little longer to get my son through school.

Asked by for the 1999 Hyundai Tiburon
Had the same problem. very easy to see the linkage is fine by disconnecting it and shifting it at the trans it self.
So I pulled out the trans and took it apart. Seems like it broke in the weakest spot the bar that connects the shift control inside the gearbox
To the 3rd 4th gear fork. I just pulled one apart at the junk yard and replaced the whole fork assembly. With a ton of work and a little bit of knowledge it only cost me about $30 to fix.