From your description the repair guy has for filled his obligations / contract.
You do say the unit stared up as expected the first time.
I think your going to understand at which point it has died first before you can point any blame. A simple fuse could have blown or a part failed within the unit. You never know, the repair person could have left a component loose thats caused a short circuit.
The gut reaction is to blame the repairer but you are going to have to get an engineers report to move anywhere forward.
No fix no fee, gets you in the door, but you actually knew the problem and that was the job, replacing a hdmi port, shouldn't be a no fix no fee. As you know what was broken.
Now the unit is broken, that is the situation i would have work done under no fix no fee.
For me an engineer reoprt is the only way you can move forward.
Check fuses, external and internal.
What do you have to loose?? Nothing.
Its your word against the repairer, unless you have a receipt for the works to be carried out.
You could get someone to take the unit back in under the no fix no fee, you never know, he could fix his own mistake, with out even realising.