The rig boots fine, whatever the number of GPUs.
It's just that one of the GPUs is not recognized by the driver. I can still see it in lspci, though.

CPU is Intel(R) Celeron(R) CPU G1840 @ 2.80GHz

Update: I replaced all GPUs with 750Tis. 6 of them. And they all worked fine.
Another pointer towards the PSU: a Corsair CS750