What happens if i replace my iphone 5c motherboard? Does it just go back to factory settings - as if it is a new phone....?

I bought a used iPhone 5c in April earlier this year. It was in very good shape and I got it for a steal. I have taken very good care of it - heavy duty case, never dropped it, cleaned it once a week, careful about letting it heat up too much, etc. It worked perfectly until July. First the clock stopped working - when the phone is locked it freezes and I lose time. This happens whether it's set to automatic or manual. Then, a few weeks later, the Wi-Fi and Bluetooth stopped connecting consistently - they may connect for a few seconds or minutes but no longer. Then the next week - my screen started to freeze up randomly for a few seconds at a time - it would turn black until i pressed the home button and it would return to the home screen. Finally - I suspect there may be an issue now with much lower battery life than before - it used to last the whole day, but this may be because I am forced to use my 3G since the Wi-Fi won't stay connected. I have tried hard and soft reset, reset my network settings, and every other easy fix on the internet. None of this worked and after doing a lot of reading on the internet it seems that this problem has happened to "lots" of other people as well. I took it to a highly rated repair shop in my area- since the genius store is not close to where I live and people online said they had no success to fix this problem by going there. I was hoping they would open it up and tell me if it was an easily fixable hardware issue - like a broken antenna. They deemed that it was a broken motherboard. I have been on the phone and in chats with apple support and I always treat them nicely because I know it is their job to be as helpful as they can but they were entirely unhelpful unless u buy the 30$ month help program. I feel like getting on the phone and screaming. I need my phone for school next week. (Sorry about the long winded tale - just extremely frustrated and maybe vented a little too much) Since I bought this phone used and it has already been opened by a third party I have no warranty to replace my phone. I am a college student with a low budget and I can't go and buy a new one - especially when my phone broke after a few months and it was entirely not my fault. My last resort is to buy a replacement logic board and see if that will fix the issue - has anyone tried this and has it worked?