What's your guys ruling for when an enemy fails to attack in melee, that the PC can use a basic weapon to fire in full auto/attack?

No. Even if a melee attack fails to land, the PC is considered to be engaged in melee. So he cannot use a basic ranged weapon.

Yeah, that's how I do it, too: if an attack has been rolled , melee is engaged, even if the attack was a miss. If, however, an attacker tries to charge, but comes up short and must run to get to base-to-base, those two opponents are not engaged in melee, and the target of the failed charge can blast away.

Thanks for the confirmation, I be sure to remind my fellow players.

RAW it's unclear imo. But I's guess it's what Adeptus B said.

I'd rule that being in melee range with an opponent who would have the ability to make a melee attack is enough to make shooting with a basic weapon impossible.

So If for example a guard hears gunfire outside the room he's in, runs out and stumbles into a PC shooting down the corridor with his Assault Lasgun this PC would not be able to keep shooting even if the guard didn't attack him yet.
He is in melee range and will attack him as soon as he's able to. That's enough.