Q: Apps Store allows to sign in but does not allow update or purchase

Just put the apps in the Trash, but don't empty it. You can retieve them later if need be. The Mac App Store can't see them in the Trash, so you should be able to redeem your codes and install new versions of the apps. If you are successful then you can empty the Trash.

Sorry, I didn't realize that you would use LaunchPad. I was thinking drag them to the Trash from the Applications folder. Dragging them to the Trash from LaunchPad likely immediately deletes them, I don't know for sure, I have never really used LaunchPad.

How are you trying toredeem these codes? What process are your using?

http://support.apple.com/kb/HT1574

Has some other Apple ID been used on this (brand new) computer by the reseller?

As long as you are not actually seeing a starnger's Apple ID appear on your Mac, them most likely no.

The issue is that you likely didn't do the setup of the new Mac exactly right. When you first set up the Mac, before using any apps you are supposed to go to the Mac App Store, sign into your account (Store menu) and go to the Purchases pane and accept the iLife apps; iPhoto, iMovie and GarageBand. If you did not do that and you used any of the three apps, then this is the type of problem that results. You cannot accept the apps and ypu cannot update them.

Do you ever get an opportunity to enter a redemption code?

Step by step what is happening when you try to redeem a code. If you can take and post screen shots of what you see (don't revel your Apple ID or password in a screen shot.)

To take a screen shot press Command + Shift + 3. By default, screen shots are saved to the Desktop. To post a screen shot here use the camera icon and browse to the Desktop and select a screen shot.

Have you tried signing out, quitting, shutting down your Mac and rebooting your modem/router, then start from scratch with trying to redeem a code?

Sorry it is 1 am and I need to go to bed.