Which man page describes the process of a computer turning on?

You're thinking of the boot(7) manual (man 7 boot) and/or the bootup(7) manual (man 7 bootup). Those are the manuals I can think of on (Ubuntu) Linux that best fits your description.

These manuals are available on the web (see links above), but the definite text is what's available on the system that you are using. If a web-based manual says one thing but the manual on your system says another thing, then the manual on your system is the more correct one for you. This goes for all manuals.

See also the "See also" section in those manuals.

This other question may also be of interest: How does the Linux or Unix " / " get mounted during bootup?

For a non-Linux take on the boot process, the OpenBSD first-stage system bootstrap (biosboot(8)) and second-stage bootstrap (boot(8)) manuals, followed by rc(8), may be interesting.

It sounds like boot(7) or bootup(7). ie man 7 bootup

You can, incidentally, search the manual via man -k <keyword> or the equivalent but more stylish apropos command.