I was in the same boat. Couldn't do any pullups in January. I installed a pullup bar in my house and put one in the door of my office. Just started doing them all the time, and when I'm out of gas I hang there. I've worked up to 4 pullups (from locked elbows... I could probably cheat more).
I agree that the Gravitron machine is useless. For me it was mostly weight loss plus practice.
Similar boat, including tendinitis and wrist problems, but overcame them. Here's how my pull up progression went:
Month 1: First attempt, jumped up, grabbed the bar and like you immediately strained a wrist muscle, tendinitis, horrible weakness and pain. Couldn't type. Took the next 30 days off and just did light cardio and slowly started eating better.
Month 2: Tried to pull-ups again. Used Gravitron back-to-back with pull-up bar at gym intermittently. At the pull-up bar, I had someone boost me up. It was embarrassing. One day, 15 days into this month, I had a really bad day at work and was really angry. I went to the gym, took off my workout gloves, and had this surge of adrenaline and did my first unassisted pull-up. I also used the gravitron to do unassisted tricep dips.
Month 3: Got up to 3 pull-ups by the end of the month.
Month 4: Got up to 6 pull-ups.
Month 5-7: Still at 6.
Month 8: I started doing "intervals" of pull-ups, i.e. 3 pull-ups followed by a break and 3 more until complete muscle failure.
Month 9: 10 pull-ups.
Month 10: 14 pull-ups!
Month 11: Commando pull-ups, 1 barbarian pull-up, and pull-ups where I swap grips in the middle of the pull-up. Varied grip spacing. On good days, 6 sets of 10 pull-ups, on bad days, 3 sets. Perfectly still and straight body, zero upward momentum on pull-up motion.
The hardest part of the mental barrier of getting to that first pull-up. It took 2 months of continual trying to get to 1 pullup, another 2 months to get to 3 pull-ups, and after that it was easy. Initially, after month three, I had really bad form, but I backed off and started working on form for a bit with a trainer until it was perfect in the mirror. Holding my body rod-still really helped my physique. Then, it got easier and easier.
Along the way, I lost more than 90lbs, 13" off of my waist (30"), got a six-pack, and got into the single-digit % fat area. I can't tell you whether it was causation or just correlation. It just all happened!