I did what you asked and System File checker said that it couldn't repair all files. I looked in the log file that it created and near the end it read:
2013-12-12 13:37:41, Info CSI 000007f3 [SR] Verify complete
2013-12-12 13:37:41, Info CSI 000007f4 [SR] Repairing 1 components
2013-12-12 13:37:41, Info CSI 000007f5 [SR] Beginning Verify and Repair transaction
2013-12-12 13:37:41, Info CSI 000007f6 Hashes for file member \SystemRoot\WinSxS\amd64_prncacla.inf_31bf3856ad364e35_6.3.9600.16384_none_9590ba64d5b91f79\Amd64\CNBJ2530.DPB do not match actual file [l:36{18}]"Amd64\CNBJ2530.DPB" :
Found: {l:32 b:4tPVbDn5hZzMwNU8vDCHgdtfpBFqoTMEZuiD++eXnwU=} Expected: {l:32 b:n520k714Uu3utHa5JGQ6HQYbZphKhlMWq5pEmfnCDuw=}
2013-12-12 13:37:41, Info CSI 000007f7 [SR] Cannot repair member file [l:36{18}]"Amd64\CNBJ2530.DPB" of prncacla.inf, Version = 6.3.9600.16384, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type = [l:24{12}]"driverUpdate", TypeName neutral, PublicKey neutral in the store, hash mismatch
2013-12-12 13:37:42, Info CSI 000007f8 Hashes for file member \SystemRoot\WinSxS\amd64_prncacla.inf_31bf3856ad364e35_6.3.9600.16384_none_9590ba64d5b91f79\Amd64\CNBJ2530.DPB do not match actual file [l:36{18}]"Amd64\CNBJ2530.DPB" :
Found: {l:32 b:4tPVbDn5hZzMwNU8vDCHgdtfpBFqoTMEZuiD++eXnwU=} Expected: {l:32 b:n520k714Uu3utHa5JGQ6HQYbZphKhlMWq5pEmfnCDuw=}
2013-12-12 13:37:42, Info CSI 000007f9 [SR] Cannot repair member file [l:36{18}]"Amd64\CNBJ2530.DPB" of prncacla.inf, Version = 6.3.9600.16384, pA = PROCESSOR_ARCHITECTURE_AMD64 (9), Culture neutral, VersionScope = 1 nonSxS, PublicKeyToken = {l:8 b:31bf3856ad364e35}, Type = [l:24{12}]"driverUpdate", TypeName neutral, PublicKey neutral in the store, hash mismatch
2013-12-12 13:37:42, Info CSI 000007fa [SR] This component was referenced by [l:186{93}]"Microsoft-Windows-Printer-Drivers-Package~31bf3856ad364e35~amd64~~6.3.9600.16384.INF_prncacla"
Does htis mean anything to you?
Just an FYI, the printer works fine within windows 8 using the Microsoft Windows driver for the 8500. My main reason for my question was the inability to re-install HP solution Center.
I look forward to yoru response.