A1200, OS 3.9, cnet.device... and no hope left

[x56h34]

Try using BlizKick and an appropriate modules for the card reset (available on Aminet). I think they are called comething like DosResetCard and CardPatch. It's basically the same thing but in different flavor, if you will.

BlizKick will also patch a lot of other things in AOS, so it's definitely worth checking out, since you own a B1260 accelerator.

[x56h34]

Make sure you stop using Aweb II. It's seriously outdated.
Go to http://aweb.sunsite.dk for the latest version.

You can even download a version optimised for your 060 cpu, and not use the all-in-one cpu solution which Aweb II is.

EDIT: I suppose you are not using a graphics card, correct? This could also be a potential reason for constant crashes. In my experience, web browsing on AGA display always produces similar results to yours with both Aweb and Voyager browsers.