How can the initial "booting" state of a computer be different at different time points?
Can anything change in a computer without the user modifying something, also while not having internet connection?


Yes, definitely - computers update their own states all the time, and some of these changes will be persistent from one boot cycle to the next.

The computer itself is a complex piece of hardware, and the operating system is a complex piece of software. Both the computer (at a hardware level) and the operating system will carry out a series of self tests during the boot process. The results of some of those self tests will be stored in non-volatile memory (e.g. in some form of registry). When the computer is re-booted, the results of the self-tests from the previous boot attempt may affect the route taken through the boot process the next time around. This might avoid a problem encountered in the previous boot cycle (e.g. by loading a previous version of a corrupted driver), but it may also introduce a new problem not seen before.

In short, part of the boot process will be a check to see if the previous boot cycle was successful. If not, there may be logic in the boot process that tries a different sequence of actions, or boots into a restricted "safe" mode.