Hi,
I sent my previous BB back to Sprint because it had audio problems. I have a new refurbished BB.

It seems to be working fine, but during the activation with Sprint tech support it was hanging a lot and taking quite some time to start up. The sprint techs recommended I call Sprint customer service to order a new one, which I tried but I ended up being transferred to someone in the Philippines a couple times, and with bad reception on both occasions.

So I gave up and tried to fix the startup problem my self. I plugged it into the DM on my laptop to kind of shock it into starting up, which worked. Now it seems to startup on it's on now, not as fast though as my original one.

So the problem I'm seeing which is not really a problem but something I noticed is the "Enterprise Activation" icon is still on the main screen after I have activated the phone and synched it with my corporate network.

The phone works great for the most part except that it takes a little longer to reboot than the previous phone, I see a white screen with a spinning hour glass, and the activation icon is still on my main screen. I get all of my corporate outlook emails and my calendar works.

Should I request another activation password from my BB Admin to do this again or just send the phone back because of these small problems?

Just hide the icon.
If everything is working... then I don't see a real problem here.

It will be your call. However I never leave it so that the activation icon is still listed there. Usually that means something didn't carry over and it could be something as small as "time zones" which I have seen take over 15 minutes to finish on our BES server. Usually if you still see it then you are not registered at least on the BES server side (emails, calendar, etc). While some may function, you may notice issues where calendar events don't sync with your Outlook (Exchange server) and vice versa. I have sometimes waited 45 minutes while it activates (mind you this can be the signal or the amount of data being downloaded.) However, I also have seen it where it stops and no longer is going through the activation process. One thing to do is remove the battery and put that back in and it should start the activation process again.

If you are close to your BES admin, best bet is you may want to drop it off and then they can get it connected to the Desktop manager and watch the BES server which is something I always do. If not, then you will want a new activation password generated, but you may have to perform a full wipe of your blackberry before you try to activate it again.

Sometimes I have had to delete a user's account on the BES server and erase all settings and data that is stored for that user for their blackberry, then perform a full wipe of the blackberry, create a new account on the BES server and go through the activation.

Just providing some information on some of the issues I have seen, but in my history of dealing with them for my company that activation should be gone once it is completely activated.

I have had the same issue and simply wiped then reloaded the OS then ran the activation. I would suspect the time it took to accomplish may not have been allowed to complete by the Sprint tech.
When you run this, if you do, let it do it's thing. Unless your corporate BES has issues it should be ok after.

As Penguin3017 stated, you may just need to hide the Icon.