hmmmm. I was setting up a cheap guitar for a friend a while back, the truss rod had very little adjustment range, I had to loosen it almost to the point of the nut coming off to adjust for 10 - 46 gauge strings. It just didn't feel like it had any tension on it. I wonder if the rod is stuck in there, like as if it were glued to the wood. Most bolt on neck are maple, which is a very strong wood, could maybe or almost work without a truss rod. In fact, I believe the first solid bodies from Leo Fender (Broadcaster or Esquire) did not have truss rods. If its a maple neck, here's what I would do:
Unbolt the neck, lay it frets down on a sturdy workbench. Use some towels or blankets to give enough cushion to where you won't bust the plastic nut. Loosen the truss rod. Put something like about 1/4" thick in the middle under the fretboard, like an extra few thicknesses of towel and then push down on the head and the heel at the same time, putting your weight into it. See if you can get the rod to break loose from the wood, if that's the problem. You won't break it.
WAIT, Before you do the above, with it off the guitar, or the strings off, put a straight edge on it. It could have "back bow" - be warped in such a way that it needs the string tension to brings it up to being flat; the rod wouldn't be a factor since it won't compensate for back bow, (unless it is one of the truss rod systems that will...) if it does have that issue, the straight edge would "teeter" on it, you couldn't make it touch both ends. If that's the case, you would maybe have to take it to a professional, or get a replacement.
One thing you could try if the repair estimate is too high, before you throw it away that could possibly ruin it -
With the rod loosened - jig it up similiar to my above scenario, maybe use something about 1/8" thick, but this time use wood clamps (with blocks to protect the surfaces from the clamp) and clamp that sucker down to the work bench on each end, forcing it into an exaggerated "front bow". Not too extreme, and make sure its flat, so you don't twist it. Wait a day or 3... or you could try heating it up with a heat gun to speed the process. After being unclamped, if this were at all successful, it should spring back from the clamped position into a lesser degree of "benditude" (I just made that word up) into a little front bow, or at least flat with no tension. that the truss rod will compensate for. I have used this method with varying degrees of success with wood pieces over the years...