Hi and welcome to forum.
Not going into reverse is a new one, usually the issue tends to be the box staying in reverse when you try to move forward in 1st. Happens to mine quite often on really cold mornings.
The reverse interlock is situated just inside the gearbox on the selector shaft itself. If its been removed it wont be the cause of your problem.
When in neutral it should wiggle freely between 1st/2nd and 3rd/4th, but when you push it further to the right towards the 5th/reverse location can you feel a little springy resistence?
If its solid, its a broken interlock part.
If not, What May have happened is that the reverse idler gear has rusted up a little. this is quite a weight and slides up the idler shaft as you move the shift lever into reverse itself.
I would drive about to get the box hot and see if that frees it up enough?
Failing that, there's an external bolt that holds the idler shaft in position that you could hit with a hammer to see if the shock releases it enough make it slide up?