I bought my computer used; no box, cant turn on, therefore no serial number access....any ideas?

You need to do a LOT more than reset the password. It is clear the last owner did you no favors. Please read What to do before selling or giving away your Mac.

To be honest if I bought it I'd return it and either buy a new Mac or buy a:

• Refurbished Mac from Apple
• Buy a used one from a reputable reseller like Macsales.com

• Restart in the Recovery Partition (hold down Command + R on startup). If you are using a wireless keyboard, use a USB keyboard for this startup.
• Open Terminal (hint look in the menus)
• In Terminal type resetpassword and follow the prompts.

SN info is on the bottom of the stand, please look there.