the shutdown issues are usually created by programs/drivers that do not cooperate with windos shutdown commands. So check what hardware was installed prior to these issues, if none, check which software was installed. Als be aware that several adware programs create the same kind of problem. Use Msconfig to prevent startup items loading the the next reboot. Then try shutting down. If all works okay, re enable a program or two at a time to eliminate the source, at a certain point something wil eventually pop up as the culprit, and if you don't need it, get rid of it.
I just got a new notebook (Dell Inspiron 700m) on Tuesday, but am experiencing some problems with shutting down and putting the system into standby. The problem only presents itself when my notebook has been on for longer than 1 hour. Sometimes when it has been on for longer than that, when I try to put it on standby, nothing happens. If I try to shut down, I get to the blue screen that says "Windows is shutting down", but it stays on that screen for so long that I just end up pressing the power button to shut it off manually. Any suggestions?