Starting with Leider (an adverb) puts it in the first position, so German uses verb–subject inversion:
Position 1: Leider
Position 2: war (the finite verb)
Then the subject: der Handy-Empfang.
This is a normal pattern whenever you begin a sentence with something other than the subject.
dass is a subordinating conjunction introducing a dependent clause with its own subject. In German subordinate clauses, the finite verb moves to the end of the clause. Here you have a modal construction, so the infinitive bezahlen comes just before the finite konnte:
“…so schlecht, dass ich nicht bezahlen konnte.”
Yes. In conversational German you might say:
Leider ist der Handy-Empfang im Laden so schlecht gewesen, dass ich nicht bezahlen konnte.
Here ist gewesen is the perfect of war, and the subordinate clause stays the same.