It looks like a permission problem:
If the error file shows Errcode 13 (which means Permission denied), this means that the access privileges of the data directory or its contents was disallow from the server. Change the permissions for the involved files and directories and start the server again. If it still fails, try to make a trace file to find the problem. See the Creating Trace Files section.
Source:
MySQL Troubleshooting Guide
You should check if that user has rights to write there..