I would find another shop ASAP. There is proper way to determine why your Blazer won't start and run correctly and guessing that it is the computer with out doing a thorough inspection and data scan is not the correct approach.
A code 34 is a Mass Air flow sensor code, which can/will cause a no start. If the wiring is broken, the sensor could be fine, but the computer does not see the signal. I can go through the other codes as well. I used to be a diagnostic tech at a GM dealer and I am not convinced by your mechanics explantions. Go to the basics, is it getting spark or fuel yes or no, go from there. I would find another shop.