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Here is VMware KB: VMware KB: VMware vCenter Server Appliance 5.0 vpxd crashes few seconds after starting

To resolve this issue due to core dumps filling the partition:

1. Connect to vCenter Server Appliance console as the root user. The default password is vmware.
2. Change directory to /storage/core and run the ls command to check for core files
   
   Note: If there are core dumps, delete these dumps and try to start the service again. The problem should now be solved.

And here is a blog post showing step by step: Share the knowledge: vCenter 5.x appliance space issue /storage/core out of space