Startup problem, home screen won't load after password is typed in

https://support.apple.com/en-us/HT203176I would not say it's a.charger problem. Are you saying that after logging in the screen goes black? First try a pram reset. Command/Option/P/R keys for three chimes at startup. Then try a safe boot by holding down the shift key at startup. This will not load all extensions, but you can access your files and apps and run safari. Do you have The install dvd as you show snow leopard as your operating system. You can also boot to that and run disk utilities to check and repair the drive and permissions. If no dvd you will have to use single user mode to run a check and repair.https://support.apple.com/en-us/HT201295