As far as your computer is concerned DosBox is no different from Microsoft Office/Doom 3/Windows XP/etc.
DosBox uses your processor just like any program. So if DosBox uses alot of processor time then that in turn causes more heat to be produced.....just like any program run on your computer.
DosBox uses your hard drive just like any program. So if DosBox uses your hard drive then that in turn causes it to spin more, which in turn will eventually cause your hard drive to fail because it's a mechanical device.
Dosbox uses your memory just like any program. So if Dosbox uses your memory then that in turn causes your memory to heat up, which in turn will eventually cause your RAM to fail if you don't have proper cooling.
DosBox uses your video card just like any program. So if DosBox uses your video card then that in turn causes your video cards' processor/memory to heat up, which in turn will eventually cause your video card to fail.
So no. Just like any program run on a computer we cannot tell you if DosBox causes your problem. It may have, it may not. Most likely it was the straw that broke the camele's back. Your computer already had the problem, DosBox just allowed it to surface. Supposedly....we still don't really have any details from your on what exactly happened and you do not seem technically enclined so I doubt we ever will......which means that you'll likely keep on blaming DosBox.....too bad.