@Destinspire I had this problem once or twice when I had a WP site, when I saw what you’re seeing on the download about it could not be verified as no signature was found it would fail every time.
The fix for me was to just wait, after a few days I would see a message about WP being automatically updated to version x.x. If a manual install/update continues to fail then waiting for it to update automatically is the only alternative.
I can’t remember if ‘Update Automatically’ is a default or WP needs to be set to do that.