Some tools:

Two types of plastic cards for scraping: An unwanted credit card & a thinner plastic card - typically this can be a membership card. Make sure that these cards are unwanted because you may damage them.

A nice prepped area - best with a sheet on a hard surface like a garage floor

Soft Scrub brand cleaner

Comet brand cleaner

Cotton Swabs

Old, but quality T Shirts

Long needles (typically called denim needles)

Kerosene

Goo Gone

Water

Clorox Pen

Compressed Can Air Duster

Make sure not to have your computer plugged in and don't "dust" your computer first because deep cleaning will just cause you to have to clean the computer again.

I have found that Soft Scrub is best for "whitening" beige or white plastic. It's best to take a two sided scrub pad and apply Soft Scrub with the "soft side". Apply liberally. Leave the Soft Scrub for 24-48 hours. Wipe off with a T-Shirt and water. A Clorox pen can be used for precise application. Comet can be used for large areas or more tough needs.

Take the "scrub side" of the pad and gently scour any problematic areas. You may want to try a little Goo Gone first. I have found that Goo Gone gel spray is best. This way you can leave the Goo Gone "soaking" for a few minutes.

For stickers, tape residue, or adhesive residue use Goo Gone and a credit card to scrape the adhesive off. It's best to let the Goo Gone "soak" for a minute or two. You may need to use the thinner card to get peskier residue.

You can also use a SMALL amount of kerosene - make 100% sure you don't get any chemicals on the monitor or dropped inside the computer or the keyboard.

I have found that water is best when applied sparingly to a TShirt to clean screens. There are LCD and glass restoring chemicals if the screen has been smoke damged or smoke hazed.

Once all chemicals have been used. Lightly vaccuum the entire unit with a drape attachment from your vaccuum cleaner then Air dust thoroughly, make sure you air dust each and every crevice or hole. If the "nozzle straw" from the air duster fits in a hole or slit ... stick it in gently and spray liberally.

You can use a denim needles to get dirt out of crevices.

The best way to clean a Vintage computer is by trying several attempts at separate times instead of one cleaning all at once.