Depends on what you want to check. I don't recall Norton Utilities having a very extensive diag.
NU had decent disk tools.
I don't remember that it would do like video mode testing to see if VRAM was working correctly or whatever. That's always been either supplied by the vendor of the video card, or maybe some special VGA / VESA mode tester. Testing VRAM extensively would almost have to be something provided by the chipset vendor.
Port testing would usually require something like a loopback plug to echo data back. Otherwise you're just testing the control registers, which isn't very thorough.
CPU testing has always been a unique utility too, like the Intel FPU test or that sort of thing.
Bus testing... well, what exactly did you have in mind? Everything connects to the ISA or local bus, so if anything works reliably, it's probably fine!