Theoretically, and under specific conditions, yes. But an accurate
answer depends upon what specific operating system you're using and how
closely similar the two computers are in hardware configuration.
Impossible to say without more pertinent information. (And, for
information on non-Microsoft operating systems, check elsewhere.)
If the OS is MS-DOS, there'll be very little problem, even if the
hardware is significantly different, although you'll need to modify
Autoexec.bat and Config.sys to use the appropriate new device drivers.
Pretty much the same applies for Win9x, although Autoexec.bat and
Config.sys aren't used. If using WinNT, and the hardware is roughly
similar, the machine will likely boot, but you'll need to spend a bit of
time installing the correct drivers.
For more modern operating systems, it becomes much more complicated.
If the OS in question is Win2K, the two computers are not identical,
and assuming a retail license (many OEM installations and licenses are
not transferable to a new motherboard - check yours before starting),
unless the new motherboard is virtually identical to the old one (same
chipset, IDE/SCSI controllers, etc), you'll most likely need to perform
a repair (a.k.a. in-place upgrade) installation, at the very least (and
don't forget to reinstall any service packs and subsequent hot fixes):
How to Perform an In-Place Upgrade of Windows 2000
http://support.microsoft.com/default.aspx?scid=kb;en-us;Q292175
What an In-Place Win2K Upgrade Changes and What It Doesn't
http://support.microsoft.com/default.aspx?scid=kb;en-us;Q306952
If that fails:
How to Move a Windows 2000 Installation to Different Hardware
http://support.microsoft.com/default.aspx?scid=KB;EN-US;Q249694&ID=KB;EN-US;Q249694
The same applies if the OS is WinXP. Normally, and assuming a
retail license (many OEM installations are BIOS-locked to a specific
chipset and therefore not transferable to a new motherboard - check
yours before starting), unless the new motherboard is virtually
identical (same chipset, same IDE controllers, same BIOS version, etc.)
to the one on which the WinXP installation was originally performed,
you'll need to perform a repair (a.k.a. in-place upgrade) installation,
at the very least:
How to Perform an In-Place Upgrade of Windows XP
http://support.microsoft.com/directory/article.asp?ID=KB;EN-US;Q315341
The "why" is quite simple, really, and has nothing to do with
licensing issues, per se; it's a purely technical matter, at this point.
You've pulled the proverbial hardware rug out from under the OS. (If
you don't like -- or get -- the rug analogy, think of it as picking up a
Cape Cod style home and then setting it down onto a Ranch style
foundation. It just isn't going to fit.) WinXP, like Win2K before it,
is not nearly as "promiscuous" as Win9x when it comes to accepting any
old hardware configuration you throw at it. On installation it
"tailors" itself to the specific hardware found. This is one of the
reasons that the entire WinNT/2K/XP OS family is so much more stable
than the Win9x group.
As always when undertaking such a significant change, back up any
important data before starting.
This will also probably require re-activation, unless you have a
Volume Licensed version of WinXP Pro installed. If it's been more than
120 days since you last activated that specific Product Key, you'll most
likely be able to activate via the Internet without problem. If it's
been less, you might have to make a 5 minute phone call.