Can a DUI be issued if there was no blood test or breathalyzer done?

A person can be arrested for DUI even if no breathalyzer or blood tests were done.  A DUI charge can be based on "field sobriety" tests of which there are several.  While not as reliable they can stand as evidence of driving under the influence in court.

Also, you did not indicate why these tests where not run.  Did you refuse them? You have that right, however, if your case were to go to trial the DA would be able to talk about how you refused the test. And juries tend to assume that if someone refused the test that they had something to hide. Also keep in mind, if you refuse the test your driver’s license will be suspended for 12 months, instead of 90 days on a first offense.

All this having been said, there are defenses that a skilled and experienced DUI attorney can put forth on your behalf.  This may result in your case being dismissed or at least having the charge reduced.  Since a DUI case triggers both civil and criminal penalties, you would be well-advised to consult with a DUI lawyer.