Notebooks are a different kind of beast. There is only limited upgradeability, and working on them by someone inexperienced can easily damage them further.
That being said, some laptops with a totally dead battery don't boot,e ven connected to power. A failed CPU fan can cause it to shut off, as can a failing power supply or connection, a dead or near dead motherboard, coke spilled on it, etc.
When you say password is where it shuts down, is that the system password or the Windows password? If it won't stay on long enough to run a test on the memory, you will have to take it out and take it somewhere if you think that is it. If you can't get it to POST, that can be a fatal indicator. Replacement motherboards, capacitors,e tc. are not advisable for a novice.
How much do ytou have in this machine and how much $$$ are you willing to invest to try to resurrect it? When was the last time it worked perfectly?