Depends what you mean by 'charger in a certain position'. I've had a variant of this on a laptop I've had. What happened was that due to repeatedly coiling up the cables around the charger, the output cable fractured, just where it came out of the charger. So I could only get a charge by wobbling the cable about, then trapping it in the magic position.
So, as a starter, see if you can borrow a charger of matching type from someone, and try that. If that works, you can get chargers cheap on ebay.
You could also try borrowing a charged battery, as a one-off, just to get your files off the machine.
If it's the computer, it is possible it's just the charger socket, and you MAY be able to get that fixed cheaply.
It's usually not really worth paying to replace the m/board - it's more cost effective to get a whole new machine.
No, your files are on the hard disk, not the motherboard. They will be retained. But if you do have repairs done, stipulate you wish the hard disk contents to be retained/returned.