My Computer would not boot/respond immediately after shutting down. I may have to wait for several minutes before re-booting.What are the causes of the problem and how can I go about solving it?

This is a bit unclear to me...
If you mean that when you boot your computer it may take some time to respond then this may be caused by a pre virus check going on in the boot sector of the computer BIOS. This can be turned off in the BIOS.

If you mean that when you restart your computer from a previous windows system and it seems to hang while rebooting this is usually caused by programs or applications not releasing the memory they are storing and also can be caused by malware and spyware and applications running in the background.

All of which can be controlled by making sure that your system is clean and free from malware/spyware. Also, shut down all the applications that run constantly in the background like kodak and music sharing applications and even office applications as well!

This may also be a sign of bad drivers so make sure all driver files are updated.
One other thing can be a failing hard drive.