Mircowave does not work after I used vinegar without water to clean it
Assuming that you were using the vinegar/water mix to clean the microwave...

No, it is unlikely that you have damaged the microwave with vinegar - unless you have pure or glacial acetic acid, you are using vinegar with between 4% and 8% acetic acid, the rest is mostly water. This is not typically very damaging to metallic surfaces unless left on for extended periods. Microwaves usually are coated in plastics or paints that are not susceptible to acidic degradation.

The pop you heard could be a couple of things - either an internal fuse has blown, or it could be the magnetron. Fuses, if present, would be found on the rear of the microwave near the power cord, and would likely be replaceable fairly easily by yourself. Magnetrons are replaceable but are usually more expensive than a new microwave when you include the labor costs of replacement.