To reset the system disconnect the battery and unplug the adapter. Then press and hold down the power button for 30 seconds. Then reconnect everything and try to boot. Are you seeing any blinking diagnostic lights or hearing any beeps? Also look at this Dell support page as it may offer more help.

Remove the memory modules and try powering up.  Do you hear a set of beeps (two) or see a flashing LED pattern?

Did exactly that.  No beeps, no blinking lights, the only thing illuminated is the Caps Lock and that is lit steadily, not blinking.

Nothing is ever displayed onscreen, so it would be impossible to run any preboot diagnostics.

Try connecting the computer to an external monitor or TV via the HDMI cable to rule out the possibility of a faulty display panel.

To add to ejn63's post, remove and reinstall the RAM modules, but insert only one and power up the computer. If it still doesn't boot, power down completely, remove that module and install it in the other RAM slot. Repeat the process with the other module if the laptop still fails to boot up. If swapping RAM modules doesn't solve the issue, then the motherboard maybe faulty and will have to be replaced.

Kflash08, you get the prize for putting me on the right track.  I had purchased a memory upgrade from Dell last year and have had no issues with it.  I removed that module and switched the module that shipped with the laptop into that slot.  Laptop booted right up.  I then put the memory upgrade into the empty slot and it booted successfully again.  This is the laptop my son uses for college and you saved the day, thanks so much!

If your Dell computer does not turn on or boot into the operating system, it is recommended that you first perform a hard reset. Performing a hard reset fixes many problems and also drains residual power that may be causing the problem.