The runaway log file per @maccruiskeen would be my first guess as well.
To make hidden files visible open the Terminal app and type:
defaults write com.apple.finder AppleShowAllFiles YES
Then restart the Finder (reboot, or press Option and click Finder in the dock and click Restart).
To find large files, go to Finder, bring up a search box (Command+F), and then in the filter area (probably says “Kind” right now) click, select Other, double-click File size, then in the next box select “is greater than” and in last drop-down box select “GB”. Then type in some number in the search field – start with greater than 5GB. Your search should look like this:
Good luck!