You can reset password of any account by booting into the Recovery Console and using
passwd command there:
after which you should be able to log in.
Alternatively, you can boot from an Ubuntu LiveUSB and use
chroot command to access to
passwd command on the laptop's hard drive as root.
HOWEVER, if you bought the laptop on ebay, I would strongly advice you to perform a full re-install of the system - using it as-is is just not safe, nobody knows what the original owner installed there.
To perform a fresh install you don't need admin permissions on the laptop - you simply put a CD in the tray or plug in a USB flash drive and reboot the system. You may need to go into laptop's BIOS settings and make sure CD drive or USB comes before the hard drive in the list of boot devices.