The last time I ran into that, it was an application that was starting up in the classic environment during boot time and crashing it could close down normally. Be sure you don't have a classic application starting at boot time.
If you are not using the classic environment or that does not solve the issue, start by deactivating everything in System Preferences > Accounts > Login Items and anything you find in the StartupItems folders in the Library folder at the drive root and in your user folder.
Next, look in Activity Monitor probably under My Processes. You can selectively quit processes until the rectangle disappears and you will have identified the offending application. Since you just installed Tiger it is likely some utility or startup application or utility that is incompatible with OS X 10.4 -- there are a lot of them due to internal changes in the OS. I have yet to run into one that did not offer a free update for Tiger compatibility.
If you don't find anything that way, go to the Console application and scroll back to the beginning of the default log file and see if you find errors or failures reported during startup.
iMac 3.06 GHz core 2 Duo OS X 10.5.8
MacBook Air OS X 10.5.8
MacMini core 2 duo OS X 10.5.8