Dude, I have some good info for you. I've been lifting like a demon for 10 years. 2 years ago I herniated 2 discs in my back so badly I wasn't even able to tie my shoes. I've been able to figure out crazy workarounds for every muscle group and am still making gains. A general rule is you're going to need to do such perfect form that light weight feels heavy.
-chest- I can't pick up the heavy dumbbells I used to. I stick to barbell bench (when I have a spotter), chest press machine, flye machine, and db flyes. If you grab like the 40lb weights and go super super super slow, stop at the bottom and push up and squeeze you can make light feel crazy heavy. I also have had super good luck with dips. Same idea, stop at the bottom, push up through your chest and triceps and use perfect form.
-Shoulders- pretty tough since we can't overhead press. Your front delt gets blasted on chest though so I view shoulder day as "middle and rear delt day" Lateral raises are pretty much all I can think of, but I just do a shit ton until I want to die. Also, rear delt flyes and laying down on bench bent over laterals.
Back- wide grip pullups and wide grip lat pulldowns. I can't do any of the machines that cause me to bend over so it sucks but I just do sets on sets of both of the following. I can normally do like 28 pullups but if you do super absurd perfect form on wide grip pullups it's a challenge to even do 12.
Biceps- I can only do preacher curl becuase everything else hurts my bitch back. I do reverse preacher curl and regular and Im making gains
Triceps- I can do dips, tricep pushdowns (spin around backwards and brace your back against the little metal bar). skull crushers
Legs- this is the toughest. All i'm able to do is holding weight lunges and sprints on the bike. Regardless, If you do 10 sets of 20 lunges holding 45lbs I guarantee you'll vomit. Especially if you finish off the workout with 4 sets of sprints on the bike for 30 seconds.
Last thing: Make sure you are picking up the weights correctly. NO bending down and picking it up like normal healthy people. Squat/lunge down, brace your core, and pick up the weight.
Finally, at least for my back I can't do normal crunches. I just pick an absurd number of bicycle crunches and then do that. If you do 600 bicycle crunches your core will be on fire!
Hope it helps and remember not to use your back as an excuse. I'm making gains and for all intents and purposes I'm about as fragile as a 7 year old girl