Looks like a nice old accordion. You may well, with patience, be in luck on the bass buttons. They are designed, as you know, to spring up after being pushed- but the springs that provide the motive force are the twelve springs (one for each tone in the scale) that operate the main pallets. When any given button is pushed down the spring involved has more than enough oomph (technical term...) to return it. When two buttons are pushed still true. But when a whole swath of buttons go down- as when the instrument is bumped hard on the backside and the sheer weight of all that metal in all the bass button shafts pulls the buttons down-the return is very weak. If a couple of those buttons wind up under the back plate (no longer lined up with their holes) or with the little metal arms on the shafts UNDER the arms on the rods for one of the notes on the pipes (the arms on the shafts of the buttons push down on the pipe arms when pushed, opening the applicable pallet and sounding the appropriate note(s)) then the buttons won't come up because they are either under the plate with the holes cut out for the buttons or they don't get pushed up by the pallet springs because the arm worked by that spring that is supposed to be pushing up is no longe under that arm and so can't push.
Since each bass button opens pallets opened by other buttons ( the primary notes appear multiple times and the notes in chords of course show up in many chords) a button shaft not being opened winds up affecting several other buttons. Fix the main culprit and the others should return to action.
But despair not! If you can cough up a long thin pushing device ( a knitting needle cut off behind the tip works fine as would any several inch long shaft with a flatted tip- ideally slightly notched or my personal favorite; a length of coathanger with a pliers induced sharp hook at one end to pull as well as push) and take off the back panel of the accordion (remove the bass strap at one end and there are a couple of screws holding the panel in) you can see all th shafts . Track down which button shafts are not going up and make sure that the button is able to go into its hole- just gently push it with the end of your rod into place. If one is stuck down it will affect several others. Getting them all in place is like one of those old "get the little steel balls in the holes by tilting a picture under glass" games (or like raising kids...). You're best advised to work on the upper rows first and to be prepared to take a few deep breaths as others will want to pop back out of their holes while you're aligning away on the next candidate.
If you're really lucky they'll pop back into place and all will be well. If not then step "B".
Start patiently checking the button shafts that are completely lifeless to see that the little arms are OVER the spring loaded arms they are supposed to push down, (working one of the good buttons while observing will show you how this works). If under not over then gently coax it back into place with your rod. After completion odds are all will be well.
At no point should you start trying to remove any of the rods unless you're prepared for substantial and very careful tracking of what goes where and prepared for REAL chaos if you get mixed up. Most of the time rod/button removal is just not needed at all and you can get things going just fine by gently poking, prodding, and coaxing. The sunk buttons phenomenon occurs pretty regularly in shipped or carelessly bumped instruments and while irksome- it is not at all serious.
Truly- may good fortune smile upon you -
Henry
PS
https://accordionrevival.com/ACCORDION_REPAIR1.php has good pictures and information. Mr B is aiming for a dgree of workmanship that is probably greater than what your after here- much of the presentations involve pretty substantial tinkering which- in this case- probably isn't required to "just get it playing". One you've done that you can branch out if you so desire.
PPS I have terrible eyes and as a result proof terribly off a screen so I apologise for spelling and syntactic howlers.
