I am running FC4 and have had no problems for quite a while. This morning I log in and do an "ls". Response: "Segmentation Fault". I change directories and do an "ls". "Segementation Fault". I hit tab to see what's in the directory... Oh there's files there all right, but not the ones I'm expecting. So, I blame the recent heat wave and consider my HDD fried. I type in the e2fsck -ycfv /dev/hda1 ... I get the message about causing severe damage repairing a mounted filesystem...

Now here's the question. I'm not actually physically at the machine. Will this actually cause severe damage? Do I have to actually make my way to that machine and do it all while sitting in front of it?

Yes, it will do severe damage. The problem is that the in-storage filesystem data for the mounted filesystem will not match what is physically on the drive once fsck rearranges it to correct problems. The next time cache is flushed, the disk structures will be updated with inconsistent information and there will be nothing but trash on the drive.

You must have the filesystem unmounted.