I had exactly the same issue.
The parking brake is unrelated. But yes, you have to replace the glow plugs, that is most likely the rootcause.
My local mechanic explained to me that, as they age (when over 100,000km), their internal resistance reduces, hence they would gradually be drawing higher current, which would trip the glow-plug-fuse.
Got all 4 plugs replaced, new fuse, and no problems 20,000km since