Post the PCN, both sides, as we don't see many from this council.
If you go on you'll be asking them to use discretion based on evidence you didn't exceed 3 hours.
With blue badge contraventions, they may have a policy to allow a first one, and they may make a more considered decisions at formal stage.
But their policy is a tad contradictory as they are less happy with a wrong clock time than no clock:
Failure to display valid Blue Badge
Failed to display
• notice to be upheld. If the valid Badge is produced the Notice may be waived but
only on one occasion per Badge owner
Expired Badge
• notice to be upheld. Discretion may be exercised if valid Badge is produced within
one month of expiry date
Badge face down
• if the valid Badge is produced the Notice may be waived but only one occasion per
Badge owner
Badge on floor
• notice to be upheld. If a valid Badge is produced the Notice may be waived but only
on one occasion per Bade owner
Clock time set incorrectly (on street only)
• notice to be upheld. Discretion to waive the charge may be exercised if arrival time
shown is less than 15 minutes from the time of observation
Clock time expired (on street only)
• notice to be upheld. Discretion to waive the charge may be exercised if time shown is
less than 15 minutes from the time of observation
Badge with no clock (on street only)
• on one occasion per Badge owner discretion will be exercised. Thereafter mitigating
circumstances will be taken into consideration
https://www.lincolnshire.gov.uk/downloads/file/2332/parking-enforcement-procedures-manual-pdfa