Start up time

You could try clearing your system Cache. On the dashboard: Settings>System>Storage>Scroll to you HDD>Press Y>Click Clear System Cache, Then restart your Xbox

Do you have kinect...uh connected? I had same problem, unplugged kinect and it boots normally.

Are you able to use a USB drive in lieu of the hdd? Perhaps the hard drive is just going faulty. I had one hdd do the same sluggish stuff before and everytime I could make it to storage under settings and begin deleting the corruption it would either freeze
in mid deletion or the corruption would return the next time I would boot the console. It kept happening until the hdd caused a general hardware failure known as E68, which relates to a bad hdd. Try a different hard drive or a USB thumbdrive and recover your
gamertag to the new device. Then boot the console into Xbox live and see if that solves the issue. This will determine if it's the console, hdd or network.

I've been having the same problem with my 4 gb 360. It takes 15 minutes to get to the dashboard and another 5 to read a game, even if the game is on the HDD. It also will no longer go on Xbox Live but goes on the internet just fine. I have done all of the
above too with no changes. By the way this is my 3rd console, the 2nd slim.

I've had issues like these, what I've tried doing is deleting things on my hard drive that I don't need. Eventually, it starts to take a while to start up and I know it's time to clear some hard drive stuff, although 10 minutes is a very long time. Usually
for me it seems like my xbox takes 30+ seconds to get to the dashboard, and that's longer than usual.