That looks like it might be the monitor's own on-screen display rather than anything Puppy related. My guess is that the monitor hasn't been detected properly and Puppy is putting out a resolution that the monitor can't deal with.
Since the message says 1280x1024, either the monitor is 1280x1024 and can't deal with anything else, or it's not 1280x1024 and is being sent 1280x1024 resolution and is complaining about it.
(Or worse, it's a clock frequency error which was a real problem back in the early days of Linux.)
As for how to fix, the answer is going to be different depending on the age of the base Linux under Puppy and the graphical subsystem.
For X/X11/Xorg it's probably going to need use of the xrandr shell command, perhaps to delete the mode that is causing the problem. For Wayland, it appears that each window manager has its own xrandr equivalent. I see talk of a gnome-randr, for example.
To get to a shell in the first place, try the Ctrl+Alt+F1 key-combo. If the computer isn't frozen, that might get a text-based console login prompt. (Puppy might do things differently here though. Not sure.)
Alternatively, look up how to boot to a single-user shell by modifying GRUB options, that is, if no such option is there already.
Caveat: I am no expert. Take this under advisement. Also try web-searching some keywords. It might be there's a really simple fix for this that I don't know about.