Nah nah nah, we're not ready to go buy a vps yet.
If there IS a problem, and there could well be one, then all buying a vps does is take everyone else out of the equation. Very nice and neighborly, yes it is, but it doesn't fix YOUR problem.
Ok, so your host says he is seeing a dozen requests for ubbthreads.php running all at once and you got a ton of popups. All, I assume, are ubbthreads.php?
If you can make that happen again, Doug, grab the entire URL from the popup. We need to know what function got opened 40 times. Even better is knowing what link you clicked to give you 40 popups. That link is the important one.
Next, let's find out if he's seeing 40 requests started all at once, or 40 that happen to all be running at the same time. By this I mean started at different times but are happen to be running at the same slice in time. Maybe some of them are running long or not timing out. What is the state of the database? Are there a bunch of ubbthreads instances waiting on the database to return a result? Does he have logging of long running queries on?
There is a lot of info to find and a little work on your part to get it, as well as your host. It could be worth it to you to find the problem and not spend the money for a vps.