I just copied this from a listing for a new battery for that particular computer
Use your Dell latitude c600 laptop'* power management features. The system will run at lower processor speeds when enabling power management features and it will go into " sleep " mode faster when inactive
How old is your battery? That might be a possibility
Do you have any peripherals plugged in? External mouse/keyboard? These can keep a laptop from going to sleep. What if you open up the microsoft configuration utility and go to the startup tab, disable everything, then restart?