As others have already pointed out, I did wrote (or indeed, any past tense verb) is never correct.
But it's also worth mentioning that I did [infinitive without "to"] is an archaic construction. Except when it's being used for emphasis. The stress is normally on the word did - emphasising that you actually performed the action (usually, when contradicting someone who's suggested that maybe you didn't), but in some cases the stress may fall on the ("to-less" infinitive) verb...
I did write to him, but I never actually checked to see if he received my letter.
(if write is stressed, probably it will be in contrast to another verb which will also be stressed).
If you can't naturally imagine heavy stress on either did or the verb following, you don't want did at all.