Other than spending money replacing a part by "guessing" which it is, you'll have to actually do the tests, at least the simple ones like voltage on primary and secondary for the PID Controller's transformer (as described in the suggested thread). If you want to know for sure what the problem is, you'll either have to do some testing, trial and error, or have the machine looked at by someone who will. The suggested thread lays the potential causes out pretty well.
If you're still looking for the guesses of others, my guess is the Gicar is failing somehow and not powering the transformer... But that's a more expensive trial and error guess than the transformer, so I would still replace the transformer first if I weren't allowed to do any tests and know what to replace.

Agreed. At this point I need the electric voltage continuity to test.

In my spare parts box for my Pro 700 (purchased 8/2021) I have an extra controller and PID. Does anyone know if these would be compatible with the OP's 2017 Pro 700? The PID is the upgraded version that lets the steam boiler heat up to 272F.

If these are compatible, and if @bridge is interested, I'd be happy to mail these off on a loaner basis to try and rule a few things out.

That is really nice of you. Yes I would take you up on that. I've already replaced 2 relays ,tank thermostat and a Tank magnet. I can work on my own machine. As you know Profitec is fairly easy to work on . That would make it easy. I'd send it back to you immediately. I will send you a private message.

I previously mentioned about the power switch, but since the green light goes ON maybe it's not.
The problem is that if the OP cannot provide any test with a multimeter, but he has familiarity with electricity, i probably try to disconnect the 12vcc power box alimentation from the gicar board, than supply 110 v separately to see if the problem is the gicar board or the 12vcc power box.
Anyway, after all the suggestions, and the OP repair attempts , by exclusion, only the gicar board or the gicar power box remain to be checked, so i hope he will soon get to the end.
Edit: anyway i think it's more possible a "tired" gicar board component that does not immediately send power to the gicar 12vcc box.
Seems more a "mechanical" issue than a real electric issue, so a relay is the only electro mechanical component i have in mind, as was mentioned many post before by another member.

Thank you all for the suggestions.

A huge thank you to Robert, a complete stranger. He sent me a Gicar CPU and Pid for my Profitec Pro 700 to see if it would fix my start up issues. Well it did. It was my main CPU. It was an easy replacement. There are good people out there and one of them is in our Home Barista group. Thank you Robert!