Your problem is inside the engine bay. It sounds like the sleeve retaining clip on your shift linkage for the y cable (the one on the right in the picture) came loose and the cable is being pushed out of the sleeve (and then flexing) when trying to push the y fork on the transmission. (Unless the cable get's caught on something, it should work fine going into 1st, 3rd, and 5th, because you are pulling the flexing cable, not pushing it.)

Get a person to try shifting into those gears while you look under the engine bay at the shift linkage and you will see exactly what I am talking about.

It's possible you could peice it back together (will the linkage out of course), but it would be very time consuming and may not hold for long.

You'll need to order a new shift linkage if this is the case.


P.S. It most likely got damaged by trying to force the car into gear (such as when the clutch wasn't all the way in).