My bathroom sink at work had water that would not drain, so I removed the trap and snaked the lines but the water still drains very slowly. Thinking it might be a venting issue but??

How far back did you snake the lines?

The snake only went in about 2-3 ft

Hi bchevron and welcome to The Plumbing Page at AskMeHelpDesk.com

The snake only went in about 2-3 ft
That's not nearly far enough. You need to run out at least 7 feet from the trap. As you go up into the wall you'll hit a bend about 8 inches in, Once past that you'll only have 6 more feet to go. Go back and try again. Good luck, tom