So, first appeal rejected means no prosecution and the second appeal can focus on the technicalities.
Quote the regulations that say when a Penalty Fare can be issued and show that your situation does not fall within any of them.
As the PF was issued from Birmingham New Street, focus on that fact.
You had not yet boarded the train so 4(1) does not apply.
Birmingham New Street is not a CTA within the meaning of the regulations so 4(2) does not apply.
Regulation 4 does not apply, so neither does regulation 5 and so there was no authority to issue the PF.
Further, you can quote the text from the notice itself starting "This is because..." which is also incorrect in respect of the journey on the notice from Birmingham to Liverpool.
Finally quote the bit about how the appeal must be processed - that they have no discretion in this matter if the facts are as stated - 17(2)(b), 16(3)(a), 17(4) etc.
You could throw in all the other errors mentioned, but to be honest this one seems so clear cut it seems hardly worth the effort.
You could begin with a summary sentence that outside CTAs PFs can't cover travel not yet commenced by boarding a train so should never have been issued.
Quote the regulations that say when a Penalty Fare can be issued and show that your situation does not fall within any of them.
As the PF was issued from Birmingham New Street, focus on that fact.
Requirement to produce a ticket
4.—(1) A person travelling by, present on, or leaving a train must, if required to do so by or on behalf of an operator, produce a valid travel ticket.
You had not yet boarded the train so 4(1) does not apply.
(2) A person present in or leaving a compulsory ticket area...
Birmingham New Street is not a CTA within the meaning of the regulations so 4(2) does not apply.
5.—(1) Subject to regulations 6, 7 and 10, if a person fails to produce a platform ticket or a valid travel ticket in accordance with regulation 4, a collector may charge that person a penalty fare.
Regulation 4 does not apply, so neither does regulation 5 and so there was no authority to issue the PF.
Further, you can quote the text from the notice itself starting "This is because..." which is also incorrect in respect of the journey on the notice from Birmingham to Liverpool.
Finally quote the bit about how the appeal must be processed - that they have no discretion in this matter if the facts are as stated - 17(2)(b), 16(3)(a), 17(4) etc.
You could throw in all the other errors mentioned, but to be honest this one seems so clear cut it seems hardly worth the effort.
You could begin with a summary sentence that outside CTAs PFs can't cover travel not yet commenced by boarding a train so should never have been issued.