Can a shop's computer diagnost a bad turbo

White smoke/steam is signs of a blown head gasket particularly if it is accompanied by coolant loss. gray smoke is a oil consumption either caused by piston rings that are worn or stuck, valve guide or valve guide seal wear. Turbo charger failure can certainly push blue gray smoke out the tail pipe. Things that contribute to turbo failure is use of inferior oil, infrequent oil changes or low engine oil level. Synthetic oil is best for use in turbo charged engines as it can withstand the high heat the oil absorbs when lubricating the turbo bearings.

I cant say for sure but it sounds like you have blown or cracked head or head gasket,ask someone to do pressure check a shop should not charge for this since most estimates are free and this should be part of knowledgable diagnosis.