Ok.. so I am so going to plagiarize this but I needed a place to find it for easy reference. What better place than my blog. If psa fails to start after upgrade it is most likely a problem with a bug in the latest openssl package. Parallels has an update here:

http://kb.parallels.com/en/8338

Basically, you need to update the openssl package. Links for the various OS's are listed in the URL. Download the rpm, install it and then restart (or start) psa. Voila. Back to business as usual. I should also note that I experienced this in version 9.0.3 of Plesk. I don't know if it affects other versions.