BeeDev,
That certainly qualifies as a 'weird one' (almost worthy of "The Daily WTF"!).
I'm staggered that your ISP aren't prepared to help you by way of logs or indeed ANY info. I would be tempted to look for a new ISP simply on that basis...
...but let's just check a couple of things.
Does your ISP offer different hosting types (Linux/Windows)?
Does your site use any server-side databases? If so, are these Microsoft DBs or (e.g.) MySQL/PostGRE SQL?
Does your site depend on PHP on any other specific technologies like ASP, Java, etc.?
Does your site have a large number of animations, audio, or video?
Is there any other thing about your site which might cause a huge amount of server-side activity (ASP pages, AJAX, RubyOnRails, Actinic Catalog, etc.)?
I expect your team have thought of most/all of this already, but it would help to know a bit more about your site. Is it commercial? Does it use any kind of 'shopping software,' for example?
And finally ... are you sure that your 'new' site is on the same physical server at your ISP as your 'old' site was?
And, I for one would love to know what the answer to your problem is, once you finally work it out!