Theoretically, you can format your 3TB disk to work with your old motherboard with BIOS via partitioning it with a GPT partition table rather than MSDOS. However, it's not totally foolproof. Some BIOSes attempt to validate partition tables when they should not and that can cause problems because of the "protective MBR" that a GPT-partitioned disk uses.
Do note that not all Linux disk tools work with GPT-partitioned disks. You would need to use
gdisk rather than
fdisk for example. The graphical Gparted and command line
parted should have no problems with this.
So, really, there's no definite answer to this. However, all UEFI motherboards should be exempt from this problem.
If you're going to be dual-booting, you need to be sure that your new Windows OS has support for GPT partition tables (see EDIT 1). Windows will only install to a GPT if a) the OS supports booting from GPT (see below table), and b) you are using a UEFI firmware, so dual-booting using a pure GPT disk not supported -- of course you could always make a hybrid MBR.
EDIT 1: GPT features of Windows versions are kind of mixed.
Windows 95/98/2000/NT 4: Lol! Not a chance.
Windows XP 32-bit: No support
Windows XP 64-bit: Data disks only (no boot capability)
Windows Server 2003 SP1+: Data disks, booting only on 64-bit IA-32/Itanium systems.
Windows Vista/7/Server 2008: Data disks, booting only available on UEFI-based systems