Flooring Tile - how to polish marble slab if spotted

I have a 4" x 7foot marble threshold, vinyl flooring on one side and polyurethaned hardwood on the other. Over the years the once gleaming surface has gotten spotted like smudges I guess form floor cleaners/waxes/foods etc. and I tried car wax and swirl remover with a hand sponge applicator no luck. I could use my orbital buffer, but I don't know what to use. I don't want to damage the marble and I want to make it EASY. What to do? Thank you.

Marble will require rehoning and repolishing to restore shine. Electroplated diamond discs are usually used on marble and then resinous diamond discs are used to restore shine. Most profesional marble restorers go through different grits when honing and polishing during restoration. A variety of grits and honing powders tend to be used.

If you are DIY, then you need to do some online research. There are several popular websites that offer pH neutral products for natural stone products. If in doubt, you can contact a professional.

Do you think any kind of cleaning solution or cleaner/polishing compound would work?

You can get stone sealers that will leave a glossy look to the stone. I bet that would do the trick. Polishing isn't a real easy process if you don't have the supplies to do it.
Good Luck
Bryan

You can do a lot of research, but DIY methods tend to offer no options.

Just to make sure that I'm on the right page, I'm hearing that some sort of dried on residue won't clean off, despite the slab being smooth and scratch-free? I would have thought that a smooth surface under the grunge would be obtainable by cleaning and then the smooth surface sealed.

If none of these will do the trick, you'll need a pro or just replace it.:)

http://www.aquamix.com/restoration.htm