The alert key compromised message refers to this update which disabled the alert system:
https://bitcoin.org/en/release/v0.14.0#final-alert. You don't need to do anything about it, except update your wallet software.
In terms of accessing the coins, the first thing I would do would be to make a couple of back ups of your wallet.dat file, if you haven't already.
Depending on the version of your client, you might find that it won't sync. You can download the latest version (24.0.1) from
https://bitcoincore.org/, verify it, and install it, and then let that sync instead. Alternatively, if you want to avoid waiting for it to sync, you could dump your private keys from your wallet.dat file and import them in to a light wallet.