Texting while driving. I didn’t do it and my cell phone can’t do it. I lost at the Court. How can I win at the appeal?

The technology you have creates a technicality the judge was not going to allow you to use to get off. Dialing a cell phone while driving is the same as texting on a BlackBerry while driving and both create a serious danger to yourself and others while you are behind the wheel.
Appeal if you wish, but in this day and time, what with 17 states firmly against your actions, I would observe you have an uphill battle.
Good luck to you.
God bless.
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First you should get a transcript of the hearing. Once you have reviewed the transcript, look for ways that the judge refused to let you present your defense. If you had relevant evidence to present and the judge did not allow you to present your evidence, an appeals court may give you the opportunity for a new hearing or trial. You should consult a lawyer in your state that is familiar with traffic and criminal law and who knows the procedures for appealing traffic violations.

First, a correction to something Mr. Brinkmeier said for anyone else that reads this question and answer so they're not misled:
California law provides an exception to the "hands free" law for dialing, so it is NOT the same.
Vehicle Code section 23123.5 (c) says:
For purposes of this section, a person shall not be deemed to
be writing, reading, or sending a text-based communication if the
person reads, selects, or enters a telephone number or name in an
electronic wireless communications device for the purpose of making
or receiving a telephone call.
As to the original question regarding the appeal:
An appeal is about procedural issues and is not the avenue to submit additional evidence, nor is it a way for the court to reweigh the evidence. If you had evidence the judge refused to consider and it was otherwise admissible, then you may have grounds to appeal. If you're intent on fighting this charge through the appeals process, you may want to consider consulting with a traffic ticket attorney. Unfortunately, the cost of pursuing this may be far beyond the fine imposed.