HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

RS, if the game doesn't launch or "crashes," it might be due to driver issues, etc. If there are "bugs with infinite chests, mobs, and other things," then this problem is almost certainly related to your WoG: you either need to reset all WoG settings to their initial values or disable some scripts one by one. People have repeatedly written that they had problems due to "faulty" scripts, and after disabling them, everything worked well (but not perfectly, since there are still errors in WoG). If WoG is not the "best" version (too old, a new unfinished one, or just a faulty "unofficial" installer), then problems may also arise from that.
If nothing helps, there is a radical solution: try playing "Heroes" without WoG (by launching Heroes3.exe). Do the problems continue, or are they gone?

it plays normally at work

If so, try copying/archiving the entire "Heroes" folder from work, and at home, unpack it into a separate folder and launch it from there – what will happen?