Make sure there is no disk in the cd rom drive if present
Also try starting the laptop without the battery installed. Take battery and try to power with just the Ac.
Also try to reset the BIOS defaults, I'm pretty sure by tapping the F1 key when you turn on the laptop will get you into the bios, look for the option to reset to defaults and then save settings and let it restart to see if you can get it going.
Another option could be to update the bios but as you mentioned, you had purchased it refurbished so I'm sure that was done but you can try again to see if would make a difference.
Lenovo Support & downloads - BIOS Settings Capture/Playback Utility - ThinkPad General
Now if you do try above and does not work, as you just purchased recently, see if there is any type of warranty that you may have and see if it can be serviced.
Hope something helps out