I can you beat a dui if they did not give you a blood test and you have ashma and blew at the precenct?

Its possible, but there are no guarantees. Asthma may be a viable defense to the alleged "refusal" to blow. You can pull the data from the machine to determine how much breath volume was blown into the machine during your actual test. This may give your attorney some valuable ammo. However, the state will likely argue that you tried to manipulate the machine and were "malingering" by purposefully not blowing hard enough. An expert on asthma and its effects may be a good idea if you can afford one in your defense.

You may have a good defense to the DUI refusal here, but you will require the assistance of an expert witness at trial. You need the assistance of a very qualified DUI attorney who is familiar with and certified on the intoxylizer machine, and the field sobriety tests. There may have been a video of the stop (not familiar enough with your county to tell you whether they normally do or do not have video recorders in the police vehicles) - if you were so drunk the officer was "afraid to give you the field sobriety test" because you might hurt yourself, a look at the video will show exactly how you appeared. Then you will know exactly what you are up against.