There are two different types of password which you can see when you boot your computer.
If you see a password screen before Windows has even started to load (at a point when your screen will look VERY basic indeed) then it's a BIOS password, which protects access to the actual computer (rather than to its operating system). It's stored on the motherboard and won't be present on a different computer if you transfer your hard drives to it.
However if the password screen appears as Windows is loading then it's protecting your operating system, rather than the computer. It will still be present if you transfer the drives if you're trying to use operating system on those drives. But if the new computer has already got a hard drive, with its own operating system on it, you should still be able to access the data on the old drives without needing the old password.
Chris