flamboyant 1's idee is excellent. Let me expand on it a little...
Well, if I was managing a site like this, the fee mentioned by flamboyant 1 would become a yearly subscription fee, and it would still not preclude losing posting rights if someone clearly violates the rules.
I'd probably make the site (at least partially, parts could be viewable without registration as a "teaser") viewable only upon registration. For the registration, I would demand a "real" e-mail address (I'd exclude free e-mail services like Hotmail etc.). Then, I would allow registered, but non-paying users to browse the site for 30 days. After these 30 days, they either have to get a subscription or they lose their viewing rights.
You would have posting rights only after your subscription payment is received.
Less traffic, but I would set the pricing to what the market can bear

, so that the contribution would be sufficient on the one hand, and the positive identification of all active posters would be a positive side effect. New visitors would not be precluded from "getting into it" - the initial registration process for viewing would have to be very simple. Just enter your legit e-mail address, click on verification link in the e-mail you receive, done.
Additionally, for special fees, you could introduce different member rankings and rights later (edit, search, special titles). Your title/rights would reflect how much you have given to support the cost of running the service. Peer pressure works wonders...
The payments received should be sufficient to at least support the following two things:
- Redesign (urgently needed, imo)
- Better board software (more stable for sure, and possibly more functions - if you pay)
These ideas are only spontaneous ones from the top of my head, so please feel free to criticize/add your ideas/modify

.