According to the OEM rules from Microsoft, if you change systems a copy of Windows [or any other software] that came with the system [i.e. pre-installed] can not be transferred to another system. So if the system dies, so does the copy.

Now, if you had changed the mobo with the same one, probably wouldn't be an issue.

But a different one is trickier. Unsure if that would be allowed.

What you can do is borrow a OEM DVD of the version of Vista you got [you can install x64 if you had x86 as this won't make a difference] and install it. Install the basic drivers you need [video, network] and use the serial number that came with the old system. Do not install any other software as it may waste your time. Try and activate. If rejected, there should be a number to call up Microsoft. Don't mention the mobo change. See what happens.

Agreed, phone is the only way that might work. I've done this with OEM copies of XP before and had success, but YMMV.