If the system is still under warranty, I would recommend you contact Dell. Also, you should check dell.com/support to see if this is a common problem via their support forums.
Sounds like you have power, but the system fails to boot. Given that, I would suspect that the motherboard is defective. Does anything show up on the display?
Try this. Remove the AC adapter and battery. Push the power button to discharge any residual power in the system. Wait 30 secs. Only connect the AC adapter (do not install the battery). Attempt to power on the system. If it boots successfully, execute a shutdown and install the battery and try again. If it boots, you may be fine. If none of these help, it may be time for a new motherboard in the Vostro.
Call Dell. You have nothing to lose if these tips don't help.
Good luck!!!