Yes, it is a legal limitation. You buy and use the software, you agree to the terms of use. 1 PC at a time.
However -
in case of a PC (motherboard) fail and replacement, reinstallation is fine.
In case of a motherboard replacement just because you want to, and an OEM license...that is completely up to MS as to whether to allow that. They are under no obligation to do so.
With Win 7, it is not written into the BIOS. What happens is, the OS reads all the hardware, and upon trying to activate, looks in the bigass database at home base. "Oh...this license has already been used on a different motherboard. Tell the user to call us to get it activated, and maybe we'll do it."
That in no way has anything to do with the OP's question:
"...can i install the 32bit version on a different computer and still use the same product key"
No he cannot. 1 license, 1 PC.
Unless you specifically bought something else that specifically allows multiple PCs. Such as the 3 pack that they used to sell.