Windows 7 No dump files being created during BSOD

To outrule drivers, reinstalling Windows won't help. Not to mention that reinstalling Windows is probably the last thing you'd want to do when solving a BSOD. Why?
Three things that cause BSOD's (from most to least likely)
- Driver/Software Issues (Graphics Drivers/AntiVirus Software etc.)
- Hardware Issues (CPU/GPU/Overclocked/Bent Pin/Static Electricity etc.)
- Windows Issues (Windows Core Drivers)

If you want to rule out drivers, use Driver Verifier (Using Driver Verifier to identify issues with Windows drivers for advanced users) (to run, Search "Verifier" in Start Menu) and wait until it crashes your computer. If your computer produces a BSOD under driver verifier, check the minidumps (or ask someone on the BSOD help forum here). If your computer produces no BSOD then you can be 98% sure that drivers aren't the problem - Driver Verifier is, in my experience, not a 100% failproof way of finding problems with drivers.

Minidumps not producing - I can think of one way around this, but it's not through the minidump files. Use Event Viewer (search through Start Menu). Under Custom Views > Administrative Events you can see errors within your system.

Hal.dll could point to a range of possible problems - If you want someone from the forums to help: Link Removed and attach the .zip to your Original Post. If you prefer debugging it yourself (nothing against that, it's what I do) then best of luck to you.