Battery died replaced now info screen not working. On start up mazda symbol in dim and back up camera is dim nothing else works. After a few minutes it shuts off. Tired to reboot but didn't change anything.

 

Welcome to the forum
A DIY hail-marry
Disconnect the negative cable and then the positive cable. Wait 10 minutes then reconnect the positive cable and then the ground cable. Note opposite of removing the cables. Avoid touching the connections multiple times when reconnecting . Then without starting the engine go to ACC (ACC position) positions and leave it there for 3 minutes. Turn off ignition and then start the engine.

Failure to follow this simple service exactly will likely fail to reset your Mazda systems.

 

This did not work after hooking battery back up and going to acc the screen came up with a dim mazda emblem it went off once and came back on dim, after three mim started no change. Is there any hope it will come back?

 

Unfortunately at this point before assuming anything you really should if still under Warranty go to Mazda. But at your year you are likely not? Then because you are USA I would look into finding an independent service shop that is ASE rated. At least you would get a service person that is certified to diagnosis the problem and then you can decide if you are capable of DIY service or having them, do it? You may want to even ask if the shop has a specific certified ASE Master Automotive technician? While ASE mechanics is very well trained and have experience, diagnostics is a little more advance training and experience level for vehicles with issue like yours

 

There is always the chance that the "new" battery is a dud and not able to reach optimum charge.
Not common, but it does happen as do the screen failures.