Can you be happy without money?
Yes, of course. Just not here, or most other places!
The fundamental things you need as a starting point are your basic necessities. Food, water, shelter, warmth. In most places you must have money to supply those. And it's impossible to be happy of you are seriously lacking any of those.
Once you get past a certain amount of money and have those bases covered, our happiness then starts to depend more on our mental health. You then need:
Company (friends/partner/husband/wife). It's impossible for most people to be happy and lonely at the same time. Does money help here? Nope. As long as you're not a scrounger, friends don't care how wealthy you are* (*if your name starts with "Lord" or ends in "Esquire", this might not apply to you!)
Purpose. We each have to find our own, irrespective of income. No doubt more money opens more doors, but at a fundamental level you can have purpose in life without being rich.
Self-respect. Whether it's hard work, or intellectual pursuits, or just being an all-round nice guy, we need to think well of ourselves. No one is happy who doesn't like himself. Money absolutely doesn't help here, but it can be a side-effect of hard work.
I firmly believe that no amount of cars, XBoxes, watches or Gucci handbags have any positive effect on happiness whatsoever.