Well, this thread generates a bunch of issues:
What do we know about booting Puppys? So I decided to review the posts and realized how difficult it is to find them. Under the "Instructional HOW TO Section" there are posts under both "Boot' and 'Install'. Maybe rockedge or someone could reorganize them placing those having to do with Booting Puppys into Boot; and leaving "Install" for those posts relating to "Installing Applications"? But even more important than that, Is there any way to make Posts a "Sticky"? The Forum is only about a year old and already fundamental information --that which everyone, but especially newbies, need to know-- is being buried under posts regarding specific 'hints' for dealing with the uncommon problem.
FWIW, my opinion is that the lead post of the Boot Section should be bigpup's "USB installer programs 0ther OS's use to install Puppy to USB", viewtopic.php?p=528#p528 which is now the 5th post from the Top in the "Installer" Section.
Alternatively, darry19662018's post, "Puppy Linux Install Howto", viewtopic.php?p=171#p171 should be first with bigpup's 2nd. "Puppy Linux install Howto" is also in the "Install" Section, fallen to 4th position.
One or the other should be edited to include a link to USBImager, viewtopic.php?p=21506#p21506 which Grey has only recently brought to our attention. [Alternatively, another Sticky should be added. What's important to note about USBImager is that not only does it come recommended but that its website reveals that it burn ".img, .bin, .raw, .iso, .dd, .gz, .bz2, .xz, .zst, PKZIP and ZIP64" to a USB-Stick and has been packaged so that it can be run from "Windows, Linux, Mac, and even Rasberry Pie". That should make it the first tool to recommend to someone trying to 'get from there to here."
Which brings me back to the specific problem raised by libertas and confirmed by jafadmin to exists: The inability to burn fossapup to a USB-Stick on a Core 2 Duo computer. I'll note that Grey brought USBImager to our attention on the Fossapup thread as a tool which has been used successfully.
For a program to work 'the stars must align': the program must function under the operating system and both must properly communicate with the hardware. I note that libertas also tried slacko7.0 and Fatdog64-811.iso, He was unsuccessful with the former but successful with the latter. Fatdog is created using a different woof version. I think by now we would have received reports of difficulty burning Bionicpup or any Puppy slightly older than Fossapup to a USB-Stick with a Core 2 Duo. But it would be nice to have confirmation that there isn't such problem. But that and jafadmin's report "This distro's init is having difficulty detecting USB drives/UUID's on pre-iSeries processors" does suggest the possibility that something has changed in woof but not for the better.
So, to answer the question libertas asked in his first post: What do you suggest me to do?
Install another older version? Yes, try Bionicpup64.