Is there a way to bruteforce the private key of this cryptocurrency altcoin? In the end of 2013 or the beginning of 2014, I bought 80 000 Applecoins (APC) for 0.1 Bitcoins and got another ten by an airdrop, so I had a total of 80 010.  I never spent the coins, and when a coinswap to a new version of Applecoin (APW) happened, I was too late to take advantage of the exchange offer, as I wasn't monitoring the coin then.

Fast forward to today. I simply could not find any copy of my wallet, and I looked on all my backup drives, simply not there. I don't specifically remember backing up the wallet, but I always do so when I run a wallet for a new cryptocurrency for the first time.

Well, all I have now is my public address and the password for the Applecoin wallet. Now the question is: Is there a chance that I can restore my private keys and basically my wallet by somehow bruteforce it?

In the Ethereum stack somebody posted a script with which he could restore his private keys just with the address and password. Is there a chance for me? Because nowadays only the new Version, APW is listed as active, the old one, in which I have the my balance of those 80 010 coins, is inactive.
First up: APC != APW. The later is a different fork, which you missed to follow… costing you cash. Besides that my research showed that the original APC coin site is down, 99.9% of its block explorers are down, and only the most exotic exchanges list APC (naming it AppleCoin, AppeCoin, AlphaCoin, etc. all using the same APC short notation) which are clear warning signs that the 2013 APC AppleCoin currency is down and out ever since they forked it into APW.

Answering the core of your question

Having said that, cryptographically the wallet recovery based only on public key(s) and wallet password is infeasible as it would mean brute-forcing your public keys to recover private keys. This is much harder (from a time &amp; resources perspective) than mining cryptocurrency, so thinking about brute-forcing is a futile effort.

The password you've got protected the database your wallet used. That's not helpful when trying to recover your private keys… unless you have a backup the wallet database — which you stated not to be available.

My advise: learn from the experience and move on… while constantly reminding yourself that regular backups of important data (all data, not only financial data) can save you from a lot of frustration and from losing money.