Why won't my Lenovo Ideapad U310 turn on and charge?

My Lenovo Ideapad U310 (not the new touch one), will not turn on since the batteries ran out while in sleep mode while in my bag. When I tried to turn it back on by plugging in my charger, the charging light won't turn on and my laptop is dead. I checked and the outlet itself is working so it's either my charger or my laptop. If it's my laptop, what should I do?