Have you tried plyometric exercises?
I used to box and we did a lot of that stuff.... like the old clapping pushups.... also we did bench press with two spotters, and we'd follow through with each rep with as much power as possible, and kinda THROW the bar up.... and the spotters would make sure it comes down slowly and controlled enough back into the hands.
The purpose of it, is to increase power throughout the entire range of movement. When you do barbell curls, for example.... you can use explosive power to get the bar up from the starting position.... but you have to slow down when you get towards the top. If you keep going throughout the entire movement with maximum power, you'll smash yourself in the chest with the bar and knock yourself over. That's just an example.... you wouldn't do plyometrics for biceps.
But things like squats if you can put together a safe setup, bench press, close-grip bench.... those kinda things. Dips as well.... you can ignore the eccentric contraction for a while, and try a few sets of dips where you LAUNCH yourself into the air (and back a little bit so you land away from the equipment).... then get straight back on, then go down, up, down and LAUNCH yourself.... that's kinda how it goes.
It's all for the same purpose. Developing power throughout the entire range of motion, not just at the starting position.
But as ballast pointed out, the things I've mentioned are all "pushing" exercises.... that's important for punching power, obviously.... but equally important is the pulling muscles.
We all know how important it is to get your hand back to guard your chin after a jab.... so of course, don't neglect your back and biceps. It's not as easy to do full plyometric exercises for these bodyparts.... so be a bit careful. It might be better to do regular exercises, but with a lot of explosive power.... but don't follow through ALL the way.... that can get dangerous.
My head is all screwed up and I'm not writing very well.... I'm all jumbled and all over the place. But what I'm trying to say is improvise and try different things, but make sure you're safe. Start things off with light weights to make sure it works okay, and protect your joints.... and watch out for the people around you if you're gunna be doing it in a gym.
Ballast is right about running.... a lot of long-distance stuff doesn't help that much. I thought I was well and truly ready for the ring after 3 months of solid training, running on the beach every morning for exactly an hour. I soon realised that long, uninterrupted periods of moderate intensity cardio.... doesn't do much for you in the ring. I recommend what Ballast said about the sprints, but it might help to even keep a slow jogging pace in between.
I'm not keen on wrist weights or dumbbells while punching. I've seen people injure wrists, shoulders and especially elbows while doing that, and I don't think it helps too much anyway. Cable crossover setups are really handy.... using the single-hand attachment, practice your jabs and crosses with some weight.... follow right through. Make it explosive.
But having said all that, I don't think punching power comes from how much weight you can lift. I would be concentrating on speed work.... I believe that power comes from speed.
My brain is dead. I hope all that made sense. Sorry.