Just to update on my adventures, in case it should be of help to anyone.
I replaced the aerosol fan (error 44:10) and after a very loooong startup, all was well. I printed a diagnostic chart which was terrible and probably showed that the heads suffered from the blistering heat this summer, as well as the fan. I know how to fix that now, so I'm ok with it and the z3100 continues to chug along. So solid.
As an aside, I had a lot of trouble finding the right part, which apparently has changed since the z3100 shipped. I was also stunned by shipping times of over a month from 3 companies. In the end, I went back to the HP site, which is not quite as terrible as it used to be, but is still terrible. After a while, I found the part on parts.hp.com. It was in stock in EU and was in my hands 2 days later. Not only that, HP didn't charge for shipping!! and ... not only that, they were the best in terms of price too! (28eur). And of course, I could be sure I was getting the right part, which ironically, turned out to be identical to the one that was installed in my machine. Ho hum. So kudos to HP for good service, even though their site makes everything hard to find.
Thanks for the help on here. Invaluable.