Can someone with 0 range make a ranged attack if adjacent to shield members to boost range?

NO.

Unless:

They are targeting someone on a different elevation.

I can't think of any other exceptions.

I've perplexed my Black Panther's range to 2 before to KO a bystander that was ruining all my plans -- I hope that was within the rules?

If you had also given them elite sniper to make them a sharpshooter. Thats a bit silly though... But you could do it! Just need super senses to qualify!

Assuming the SHIELD guys are friendly, yes they can. If they were opposing, they couldn't use the TA anyway...............

Totally. Its the adjacensy thing that is wrong. Unless you have sharp shooter yu can't range attack an adjacent figure.

I think the OP is mentioning adjacency to refer to the SHIELD members to boost his/her range. They're not adjacent to the target.

So yes, friendly adjacent characters can use the S.H.I.E.L.D. team ability to increase the range value of a character with a 0 printed range value to allow that character to make a ranged combat attack. (Maximum range value is 3 due to the Rule of 3.) And what Amora's_best_friend did is within the rules.

Also, the Zombie Spider-Man from Supernova has a 0 range and EE. The only other way to get it is with Mjolner.

If you can carry objects, you can also throw them regardless of your range value... tends to be forgotten sometimes.

Sorry, gonna have to nix this combo.
The bolded condition is clearly not met with a 0 range figure, so a ranged combat attack cannot be initiated.

And Super Senses. He's just begging for Elite Sniper.

Well done.

The first time I saw this was with the old Solomon Grundy. He was on the ground next to a building on the "four corners" map. His range was Perplexed to 1 and he smoked the Robin that was taunting him. It was beautiful.

Is this because S.H.I.E.L.D. is activated when the character makes a ranged combat attack? But since the range was 0, no ranged combat attack can be made.

How about with Perplex? Can Perplex be used to increase 0 range to make a ranged combat attack?

I see where you are coming from, but once you perplex/SHIELD to increase the range by 1, the range is 1. Since it is no longer 0 a ranged attack should be an option.