First off, awesome question! It's always nice to hear about someone with interest in the field.
Ask Patents is a graduated site in the Stack Exchange network, and it has a decently long history, but it's still in its infancy in a lot of ways. That's good in some ways for your position, and it's bad in some others.
That causes a few interesting scenarios that don't require a ton of prior knowledge to help with:
Prior art searches
I mention this since you did. Prior art searches are still a main function of Ask Patents, but we've steered away a bit from that focus since the site was started. These days, we're keen to help people with those, with interpretation of claims, and my personal favorite, with understanding the patent process. So if you can take part in doing searches, great! But if you aren't able to find anything, don't feel bad, because there's lots of other stuff the site can benefit from.
For what it's worth, though, I wouldn't be so quick to assume prior art searches are always hard. There are certainly some that are, but a significant portion of new posts on the site are by people who, through no fault of their own, don't understand the text of (or even how to read) the patent they're looking at, or may not be immediately familiar with the domain.
If you keep an eye on new questions coming in and look at prior-art-search ones, you're likely to find several that have pretty straight-forward answers that just require reading the claims.
Once you get used to reading claims, I bet 50% of the questions we get should be within your reach.
This is "that boring answer" everyone has to give when a user with little reputation asks to help out. By suggesting edits to existing posts, you'll be able to bump up your reputation considerably, and begin having the ability to do more interesting things. If you're anything like me, you might actually enjoy it, too.
This is also a great way to get familiar with content on the site, which is good for learning, and for duplicate searching.
People get directed here from all around the web, many without any experience with Stack Exchange. This is great, because we hear from people in a variety of positions, but sometimes they need some help understanding our scope and site rules.
Once you have the ability to flag posts, doing so is a great way to optimize the time that Robert Cartaino and I spend on the site. If you see something that's off-topic, let us and the close voters know via the appropriate flag, and it will be prioritized as something we don't want on the site.
This is an administrative task, I know, and it may not sound as exciting as posting or directly helping people, but it can actually be really enjoyable seeing the site get cleaner.
Another simple one, but easy to overlook. You say you don't have much expertise with patents--most people don't--so if you don't understand something, ask! That's what the community is here for. If you're able to ask meaningful and relevant questions, we'll be that much more likely to attract experts who can help grow the site. Don't even be afraid to cite other questions or answers you read, if you want clarity on those. There's a fine line between things that should be comments and new questions, but as long as you stay within scope, it shouldn't be a problem.
And of course, for answering, many questions we get stem from similar general roots: "when does this patent expire?" and "what do these claims mean?" are just two examples of things you could get good at answering, or marking as duplicates.
Ultimately, I think the best way to be successful on any Stack Exchange site is probably just to keep an eye on new questions, answer what you can, and read answers on what you couldn't. It doesn't have to be as tedious as that may sound, but pretty quickly, you'll start learning more and realizing that a lot of questions aren't actually out of your reach, be then prior art searches or otherwise.
As a closing thought, then, I just wanted to say: anything you do here will make a difference. Everyone makes a difference over on a bigger site like Stack Overflow, sure, but on a site this small, you could very easily make a noticeable impact in the general quality of content you see on the site.