Thank you, my good friends, for your additional suggestions. The fact is, however, that since I decided I would take note of the failure percentage I have not had a single failure any more: 16 startups so far, no "freezing". So it appears that the problem, like nosparks reported in one case, went away just as it came in. But I can assure you that I was really worried, when I first saw it, as I feared it would worsen, as usual in similar cases. This is why I have not tried to disable addons, as warlock suggests: if it works correctly with addons enabled, I figured it would "a fortiori" work correctly with them disabled.
While waiting for the beast to wake up again - and hoping it does not -, I like to comment on the latest posts.
MrCmonkeeDo suggests a possible PS failure caused by electrolytics. This is certainly a possibility, as electrolytics notoriously do not like high voltages, which are however "built in" in modern switching PS. I tend however to rule them out in my case, since this, in my opinion, would show up in frequent failures, which was indeed the case in MrCmonkeeDo case.
germ-x's , on the other hand, might have a point: a video card failure. Here I must report that, in very few cases of startup failures - may be two or three times at most - the startup phase would stop earlier than I reported previously: i.e., after the desktop came up and the various icons began to appear, the process would stop and freeze, with many of the icons incomplete: only a white frame for a number of icons, both on the desktop and in the taskbar. A comment by germ-x - or anybody else of course - on this would be much appreciated.
To complete the picture here is some information on my system: it is a 32bit desktop computer, which I bought from a local assembler, with the only addition to the standard version of a second HDD which I use for backups. The main components are as follows:
MB: Gigabyte GA-G41M.ES2L
CPU: 2,33 GHz Intel Core2 Quad
HDD: Two Barracuda Seagate/Maxtor disks, 500GB each, SATA
RAM: 2 x 2048 MB, Kingston
Video card: NVidia GeForce 9400 GT
Power Supply: 430W
Optical drive: Optiarc DVD RW AD-5240S ATA