When I try to launch the game it immediately crashes and I after launching Visual Studio Just In Time Debugger I get the following error report:

"Unhandled exception at 0x00CDEAEC in SR2_pc.exe: 0xC0000005: Access violation writing location 0x0000003C."

What could be causing this, and more importantly, how to solve this problem?

The first two entries in IdolNinja's FAQ should cover this.

I tried deleting the settings.dat file but the game still won't launch, nor does it create a new settings file to replace the one that was deleted. The modded settings file rar linked in that post does not open in 7zip, I get and error message saying "invalid command line" like something like that.

Having downloaded the game on GoG Galaxy I don't have the option to check the integrity of the game cache as is suggested in that post.

I also do not understand what this means:
"Add the following parameter to startup to force the game to start with default settings:
defaults"

It means getting a shortcut to Saints Row 2's exe and adding the parameter at the end of the Target entry in the shortcut's Properties (outside the quotation marks)