Hi, my iPhone 7 stops charging a week ago and now is completely out of battery.
Apple quoted me $400 to repair the motherboard which I think it's a bit unreasonable.
Any shops recommend to check if its the charging port or motherboard issue? My budget is only $100 Max considering it's a old phone without warranty
A few mths back my 7 Plus had similar issue but able to charge. The problem is one fine day it just cannot turn on and after plugging in, took a while before it starts charging. I was baffled as in how come suddenly from full batt, turned phone off and next day cannot turn on.
So I charged to full and to my horror it drains battery ridiculously fast and even drains when it’s off!

I did restoring the phone 3 times to no avail so I thought was batt issue. Took it to Apple Store, they ran diagnostics and found no problem, but I insisted they do a battery replacement ($38) and collected back after 3 hrs.
Brought home and used, but problem persisted. So I brought it back to Apple Store and told them still persisting. In the end they said could be motherboard issue and the only was is to do a full unit replacement. So I agreed and paid $491 after deduction from the $38 batt replacement I did earlier on. Since then, no more problem.
So for your case and in most cases, a motherboard problem means a full unit replacement. If you don’t wish to pay for that, just get a new phone instead.