Question 1 - In the time your car was untaxed, where was it parked?
Question 2 - Ask the DVLA to post documentation that includes details of all amounts/dates/reason for the added costs. Also ask for copies of any letters ect relating to the fine also sent so you've got dates and also know exactly for what reasons the £640.
If you qualify for legal aid, then once getting everything above from DVLA, go and see a solicitor for their advice, and if you have any grounds for appeal then he can appeal on your behalf, best option if any of your appeal being successfull.
Or, get in touch with money made clear, which is FREE debt advice and would be something you could follow up today based on what information already mentioned and find out if you have any grounds for appeal or if the fine's not disputable and , now £640.00, that is what must be paid end of.