Without knowing the model of laptop you have, or its operating system, or the model and type of the speakers or how they are connected, I would say try reinstalling your audio driver.

XPS 17 (L702x)

Windows 7 Professional

The speaker type is irrelevant because nothing works in the plug unless it is plugged in while booting up or rebooting.

I cannot even get my ear buds or headset to work unless it is plugged in during the boot up or during the reboot.

The speaker type is irrelevant

The facts are irrelevant to you because you are sitting there in front of the problem. It is all laid out for you and obvious. However when all you share is that your external speakers don't work unless you reboot, the forum members who might be able to help are left almost entirely in the dark.

The might assume that you have a Dell laptop computer, because you posted on the Laptop Audio board, but because about 20% of the questions we get belong on a different board even that is not a safe assumption.

They might assume that by "external speakers" you mean analog stereo speakers, but the regulars on the forum know that making assumptions like that is foolhardy. You could have surround speakers, usb speakers, or digital speakers connected through a s/pdif dongle on certain models. Without knowing your computer model you could have either 1 or 2 speaker jacks, or 3 jacks if you are configured for surround sound. No one could possibly know from your initial post any of these details.

In the future when asking for information, be generous with the information you share. It  doesn't cost you anything but being stingy can cost you an answer. No one wants to have to pull teeth to get to the details.

As far as your problem, it is probably a driver issue but there could be a problem with the impedance sensing circuit that switches the routing of the audio signal. I have already advised you of the first step you should take -- reinstalling your audio driver --  but you have not bothered to reply to that. Of course it is your choice if you want to follow advice or not, and of course folks can choose to not bother giving any.

Correct me if I am wrong but I believe I did tell in the post prior to your reply that my system was a XPS 17 (L702x). That is a laptop system.

I also told you that it did not work with my ear buds and my headphones. I thought that narrowed it down the the jack that I was using.

Is there any other information that I am forgetting or need to clarify?

Suggest you start a new thread and I will stay out of it. Just remember to put all of the facts in the initial post for best results, and if someone asks for more information try to avoid telling them how and why their request is irrelevant.