Logic board replacement or repair (for booting issue)? I have a 2012 MacBook Pro 13 inch non-retina model .

The issue was ,from past one year I used to get service battery message but I still kept using without worrying about it.  

The OS  would boot sometimes or else it would not boot at all showing flashing folder with a question mark. Then I upgraded the hard drive that came with the device with an SSD thinking I would solve this problem by updating the OS to Mojave which runs on APFS system which they said was good with SSD. The booting issues were still there. I upgraded the battery thinking it would solve the booting issues.But only after which it did not boot at all.

The battery was either always full or didn’t charge at all it was very confusing because the MagSafe cable was green all time the os was very slow even if it booted.

Took it to an Apple authorised service centre where they say even after changing the hard drive flex cable the booting issues are still there.

They can any time call me to take back the MacBook(as it was)as it’s been 2 months they’re working on it but no solutions found as I am being updated by them on a weekly basis.
I would trust the technician that opened the mac, replaced some parts and knows what they’re doing. Apple training is very good at fault isolation and repair skills and accurate quoting. They would likely have tested a battery or offered you a battery swap which is the typical part failing when the board won’t charge a battery.

The cost of becoming skilled enough to repair a logic board is why it’s almost always cheaper to get a service part from Apple (which you can’t do anymore due to this being vintage/obsolete) and having Apple rework the part and/or scrap it for a new logic board when it’s uneconomical to repair your board.

Unless you can get 5 Macs for scrap prices and try swapping and hope you hit the lottery, swapping the board for one that’s good is going to be the only chance you can get a cheaper repair than paying an expert to source your spare parts or perform some diagnosis on what’s failing on your specific board.