iMac shuts down randomly

[NYApple19]

My new iMac has been shutting down randomly since friday. It seems to shut down right after I turn it on. Sometimes the apple logo appears when booting up and then dies instantly.
It's the new 21.5 3.06 GHz iMac. (Bought it a little over a month ago)

I called my local apple store and they told me to bring it in. I'm wondering if anyone else had this problem or if there is a quick fix for this. I really don't want to bring in my iMac to the store.

 

[Hellhammer]

Try SMC and PRAM reset. Sounds like it might be a faulty logic board or PSU

 

[NYApple19]

I've tried resetting both of those but neither worked. I guess I'm just going to have to bring it to my local apple store.
Do you think they'll let me exchange for a new one?

 

[Hellhammer]

Do you think they'll let me exchange for a new one?

Usually Apple tries to fix it first.