macbook with mac OS 10.5.- not booting past apple logo
Firstly the blinking led on the front would have blinked 5 times, indication that the battery has problems or can't be seen by the computer. You should replace the battery or have it tested by Apple.

Also regarding the startup failure, you can hold down "CMD V" which is verbose mode and this tells you what the computer is doing in the background whilst booting up, so if you have a hard drive problem then you might see messages in verbose mode like "I/O error"

To fix the issue, boot up to the installation disc "grey disc" and use disk utility to verify your hard drive.