Apply a haze remover to clean off the film left from grouting porous stone tile. Prevent the haze problem with grout release, applied before grouting. Leftover grout haze can be difficult to remove.
Grout haze comes off slate that's sealed with grout release, but it leaves unsealed tile looking dull.
If, after grouting, you're left with a grout residue on your new slate, giving it a gray, lifeless appearance, take heart. Normally, a Scotch-Brite pad, water and a little rubbing will remove grout residue and the hazy appearance it causes. Since nothing you tried removed the grout haze, I'd guess that the slate probably wasn't properly sealed before the grout was applied. Porous tiles, especially a stone such as slate, need up to two or three applications of a special grout release. Tile and stone sealers will work sometimes, but not always.
Try using a grout haze remover, which is available at tile stores. It's not always effective on slate, however. If it doesn't work, chances are the grout haze isn't removable. Call in a professional tile setter for a final assessment. By the way, muriatic acid usually makes this situation worse.