Usually a hard reset (Hold switch to on, then to off, then keep Menu+Select pressed for about 30 seconds) will get it to repond visually again.
Alternatively, you may need to charge it for 48 hours+. And leave it alone whilst it's underdoing that charge period. Don't keep "checking it" to see if it's helped.
Finally, take it back to apple if all that doesn't work. If it won't turn on, and they refurbished it - it's their responsibility to make it go again.