Question : Problem: mini mac seems to reboot.

I've a mini mac with 10.5 leopard installed. Today the mac does not show the finder and all the icons on the desktop. I cannot shut it down normally because the menu does not appear and all the icons and the menu seems to appear and disappear constantly.
The mac finish its warranty today...

Answer : Problem: mini mac seems to reboot.

If the top two do not solve the issue,

Try booting from your Leopard DVD (osX 10.5)
Go to the utilities menu at the top and select Disk Utility
Select your disk on the left side and then click "Repair Disk"
After that operation has completed, then click "Repair Disk Permission"
This will repair any disk errors or wrong permissions (very, very common)