I know I'm a little late. I'll drop some advice anyway.
I'm a little confused. You say "my bench is maxed at 100lbs". Is your bench press maxed at 100lbs, or are all of your lifts maxed at 100lbs? Because if only your bench press is maxed at 100lbs, then obviously, you can keep hitting your other lifts with that weight; squats, deadlifts, rows, etc etc.
If you want a better burn on pushups, elevate your feet. It'll shift more of your body weight to your upper body. Use a couch or chair for starters, build up to using the wall. Dips are good for hitting the outside of your pecs, too, in my opinion. If you need to, toss the plates on or lay the barbell across your lap for added weight.
As for doing pullups. Lifts to do: military/shoulder press and shoulder shrugs for the upper back, rows (bent over, one arm, whatev') for your lats. Keep hitting your chest with pushups or benching or whatever, and keep hitting the squats, of course.
In terms of actually practicing and preparing for pullups, there's a couple options. Have a partner hang on to your feet/legs and help push your weight up a little bit. Another thing to do is jump up to the climax of the pullup, and then slowly and very controlled, lower yourself down, and repeat - ie. reverse or negative pullups.
Hope that helped a little bit.