I started working on coloring a drawing that I scanned at 600 dpi, it's resolution is 5440 x 7187.
The problem is it slows down my computer and I don't know what to do to fix it.
The file is currently at 2.2 GiB and that's just one color per layer with one layer having two shading layers
I am trying to make sure I'm not doing something wasteful or I have the wrong settings before I consider buying new hardware.
I have the Open GL turned off, hardware acceleration is turned on, and I have the memory and file size limits set high, I have about 8gb of ram.

I am not really sure if I am working at two big a size or if I am using memory from another program that ran earlier.

I was thinking maybe I should get a graphics card either by salvaging it from an old pc or more ram, again hopefully from an old pc.

Relevant specs
Windows 10
Intel Core i7 3.60 GHZ
8gb ram

Any advice would be appreciated.

Yes, you're working at too big a size. I'm not sure what you mean with "shading layers", though.

As Boudewijn mentioned, is too big "chunky" of a file, there a couple of things you need to look into, cut the dpi to 300 and make sure your color-space is the default on Krita, make sure your depth is 8bit. Of course, unless you strictly need those on different settings, then there is no much that hardware could do, you would be then looking into a very heavy-duty hardware components in order to work smoothly on such files.