You can reset a firmware password by changing the RAM amount in the MacBook, then boot while resetting PRAM. Let the boot chime sound a minimum of 3 times, and the firmware password is reset (if there is one)
You need to do a little more research on MacBooks....
One difficulty that you would have with Apple's hardware tests on MacBooks - each logic board generation takes a different version of the hardware test, and as near as I can count, there's 7 different versions just for the model called A1181. The various versions of the hardware test will only work on a single logic board type, and not on any others, AFAIK.
And - although some of the grey installer disks will actually boot several different MacBook models - booting does NOT mean that you can install the software, but you can run utilities, such as Disk Utility to erase a hard drive. Then - if you try to install OS X, it just tells you it can't install on the computer (so you have the wrong installer version)
MUCH simpler to use a commercial OS X installer (one of the black label disks for 10.5)
If you can find a 10.5.6 installer (the last one), then you can install on all A1181, although probably not the 2009 MacBook models...
Notice I don't mention 10.4 (Tiger) - Apple never released a commercial version of Tiger that would install on an Intel Mac. You can't install Tiger on a MacBook, unless you have the exact DVD that originally came with that MacBook, or the exact same disk that came with that model. And, three different MacBook models came with some version of 10.4
MacBook (the original)
MacBook, Late 2006
MacBook, Mid 2007 (which happens to be the only model that your AHT 3A128 will test)
As always, Mactracker is a great knowledge base for this kind of stuff.
There's other sources on line, but I like Mactracker.