Dealt with this a couple months ago.

If you along that cable that you said had slack, you'll see its held into the door with some push pin type connectors. Make sure all of those are pushed into the door holding the cable tight. They fall out sometimes and the cable will get caught when you try to roll the window down. Try rolling the window down with the door panel off and you should be able to tell if this is your issue.

Next thing to check is your window switch. Not hard to get to or take apart you just have to pull the center console. Sometimes the tabs on the switch that catch the actual circuit board "switch" can break leaving the window buttons useless. Since you're lights are dimming when you press them that probably isn't the issue but you can check just in case and to see what I'm talking about for future reference. It'll break at some point. There are DIY fixes on miata.net or you can buy a new switch from treasure coast for 40ish bucks.

I wouldn't think it would be the window motor itself because it would be pretty strange for them both to give out on you at the exact same time. If the cable and switch are both fine my next guess would be some kind of wiring issue but that's beyond my knowledge of these cars.