With all due respect to John

I'm going to go out on a limb here and suggest what might be an easier fix. The reason you ran out of disk space is probably due to the fact that a bug in Zimbra 4.5.6 (maybe other releases) but fixed in 4.5.7 had super-duper-verbose logging going on, resulting in a couple of log files (I know one was /opt/zimbra/log/zmmtaconfig.log) that grew about half the size of Manhattan in no time flat.
You might try just reinstalling 4.5.6, and just deleting zmmtaconfig.log from your backup before reinstalling it. Then you can upgrade on top of that (now working) install--presuming, of course, that with the freed-up disk space it IS working.
But while you're at it on a new install, you might want to consider making more than 10GB of disk space available. That seems a tad tight to me, particularly no more costly than hard drives are anymore.
Cheers,
Dan