Transmission very difficult to shift into gear

My vehicle has a 4 speed manual transmission which has become very difficult to shift into gear. The clutch feels just like before, but the shifter refuses to get into any gear. The clutch has never had strong tension, but I thought that was normal. Sometimes I can force it into gear (reverse grinds), but sometimes it's impossible.

I tried adjusting the transfer case position to N, 4L, 4H etc, and then the it shifts like everything is okay when I move it back to 2H. While on the road, it shifts okay, except when I am fully stopped. Then I have to move the transfer case back and forth before it shifts again and I get going. The gears also feel like they grind sometimes when I shift on the road. The problem seems to resurface unpredictably when stopped or while in motion.

Sometimes, trying to shift into gear when stopped feels like something is blocking the shifter and the jeep lurches forward a little bit. The best way to describe this is it makes a thud sound and feels as if the jeep was given a smooth push.

Where is the first place I should start looking? Are these symptoms of any particular problem?