Maybe I shld try sweeping (.. a new word I've learnt) the coin into another account to see if it's legit....
I wouldn't. In doing so you remove the ability of the real owner of the funds to move the funds themselves once they realize what has happened, assuming of course they have another back up of their wallet somewhere they can access. Given that this is probably going to be the most likely scenario in which the real owner is reunited with their money, then by sweeping the coins you make it significantly less likely they will ever get them back.
What would you do if you were in my shoes?
For starters, I would stop saying any more about what the wallet looks like, where you found it, how it was protected, etc. If the real owner finds this thread, then you need some way of confirming it is them, and that will probably be done by them describing in detail what the wallet looked like and the circumstances in which it was found. If you give away all the details, then it becomes too easy for someone to fake that information.
Secondly, I would verify the private key does indeed lead to the address on the wallet. I would do this on an airgapped computer as mentioned above by Loyce. I would never enter the private key on an internet connected computer due to the risk of theft.
Thirdly, I would make up a back up of the wallet. If it is already damaged as you say, then I wouldn't want to risk being responsible for damaging it beyond recovery, especially if it the only way for someone to access their life savings.
Fourthly, I would poke around in the history of the transaction which funded the wallet to see if I could find anything useful which might link the wallet to a person or centralized exchange.
Lastly, I would post the public address here to increase the chance of the owner finding it.