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The Theft function normally would have nothing to do with 'dynamic' engine performance because the PATS system is a way to 'enable' the PCM function only and not have any effect on the PCM's normal functions. This is the Theft protection.
The roughness is a second issue.
The only possible way for both to be affected at the same time is an electrical issue common to both such as the ignition switch or PCM power relay.
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The flashing Theft lamp could have a dash code associated with it that may give a tech a clue what to look at.
Dash codes have thier own procedure for read out on the dash speedo. Unless you have the codes and procedure, it is of little value at the moment.
Good luck.