re: so, my 3 week old Lenovo isn't booting up

First, check the reset button (if there is one) and make sure it's not stuck/depressed into the chassis slightly. Unlikely as it is, that's happened to me once and caused a similar boot loop.

If it's powering on, then powering off/resetting and turning back on over and over, and during all this time you see nothing on the screen (no POST), it is likely a problem with power delivery within the motherboard. That often means the motherboard itself has a defect (or something as simple as a short), but can also be a problem with a 12v rail on the PSU or (far less likely) a defective CPU. There's also the possibility of RAM, but a typical symptom of bad RAM with standard JEDEC specs is simply no post rather than constant rebooting.

I'd tell you to do a whole bunch of shite to check, but this is a 3-week-old retail build. Lenovo or Best Buy (or wherever you bought it) needs to take care of it.