Found the cause of the problem. The short version is: Remove capacitor C4 from the new A604n if you experience startup problems - see first picture.
Warranty will not be affected by this! Please only solder on the card if you really need to. Mind the prime directive: Never change a running system.
Long version:
When doing some research on the Amiga chipsets, I found that Agnus and Alice tend to get blitter problems if they have been in use for a very long time (>15 years in heavy use). It appears to be an ageing problem, and I have no idea what the underlying chemical theory is - it's just an observation so far.
As I described
here on the German A1k forum, I have been able to revive an A1200 board where I thought that Alice is defective. In reality, only the negative bias voltage was flaky, and I have been able to fix that with an added capacitor on Vbb.
Later on, I checked an A600 that displayed a similar behaviour: Blitter problems during a "Sanity" demo (Arte is one of my favourites!). I was able to fix that with a small capacitor on Vbb - without the need to exchange the Agnus chip.
This has led me to the decision to add a Vbb capacitor to the new A604n design. However, not all A300/A600 boards actually have a Vbb-capable Agnus! My A300 is equipped with an Agnus type that outputs a 14MHz clock on the Vbb pin, which of course doesnt like to be loaded with a 100nF capacitor. Once the cap is removed, it works fine.
I have added a few pics of Agnus chips - just for you to see the difference between Vbb-type Agnus chips and non-Vbb types.
Jens