Brand new iMac - Powers up, shows apple, then screen goes black.

I just bought a brand new iMac today as a gift for my mother. I was trying to set it up and get everything working before introducing it to her, but ran into a problem I can't figure out how to fix. When I power it up, it either repeatedly powers up and then shuts back off, or it powers up, shows the Apple logo, then drops to a black screen. In either mode, it is unresponsive. I have tried all the suggestions in the instruction manual for resetting it and interrupting this freezing and powering cycle, but nothing works. I have seen on another thread that this is possibly a problem with Leopard and Apple has some patches to fix it. The problem is, I can't even get the machine operating to the point where I can get to the Web to download those patches. Any suggestions? I tried calling Tech Support, but it was after hours. I'm hoping they offer Saturday help.
 
sad I’m disappointed.
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