Old iBook problem

I have an old iBook that stopped working. The screen it totally black. When I reboot it, it makes a very low pitch chime noise. I know almost nothing about macs.

Is this noise normal? It is not a very pleasant noise, so I thought that perhaps it was some kind of diagnostic noise. I read somewhere that iBooks had problems with the logic board dying, is this noise and the dead screen symptoms of that?

Can someone please point me to a URL that has some diagnostic procedures I could try before I go buy a FW cable to hook it up to my monitor?

Thanks!