This is going to sound very random, but try it and let me know if it works.

While the laptop is plugged in, remove the battery and try to run off of your AC adapter.

If that works then fiddle with shutting down the computer, and applying the battery again to see if it works. I have the same model at work, and came across the identical problem that has happened twice. By plugging it into the AC adapter and then removing the battery while plugged in, then trying to use it (sometimes it powers down and needs to be restarted, sometimes it continues to startup) then plugging the battery back in after it's powered down and unplugged from the wall has fixed it 100% of the time.

The diagnostic procedures from the Dell User Guide are as follows:

Total Power Failure When Using a Battery
If an AC adapter is not connected to your computer, the computer's power source
is a battery. If the battery indicator flashes amber or is a steady amber, the
battery needs to be charged. If the battery is flashing green and amber, the
battery may be defective. To troubleshoot this problem, use the following
procedure.
1. Turn off the computer and peripherals, and disconnect them from AC power.
2. Reseat each installed battery by removing it and then replacing it.
3. Turn on the computer. Does the green power indicator light up?
Allow one minute for the computer to initialize its components before checking
for signs of power.
Yes. Continue to step 4.
No. Use the AC adapter to connect your computer to AC power. If the computer
operates normally when using AC power, go to step 7. If the computer does not
boot when using the AC adapter, see the previous subsection, "Total Power
Failure When Using the AC Adapter."
4. Does the battery indicator flash amber or show a a steady amber light?
Yes. The battery needs to be charged. Go step 5.
No. Go to step 7.
5. Connect the computer to AC power, and fully charge the battery.
For instructions, see the topic titled "Charging the Battery" in the online
System User's Guide.
6. As the battery charges, does the green battery indicator light up?
Yes. Go to step 9.
No. Go to step 7.
7. Is the battery indicator flashing green and amber?
Yes. Your computer may be in a hot environment. Charging the battery in this
condition may affect the life span of the battery. Continue to step 8.
No. The problem is resolved.
8. Disconnect the computer from AC power. Is the the battery indicator still
flashing amber?
Yes. You may have a defective battery. Continue to step 9.
No. The problem is resolved.
9. Remove the battery, and press its test button. Is the uppermost indicator in
the charge gauge of the battery flashing?
Yes. You have a defective battery. Continue to step 9.
No. The problem is resolved.
10. If a spare battery is available, fully charge it, and then install it in the
computer.
11. Turn on the computer. Is the power indicator off?
Yes. Your original battery is defective. Call Dell for a replacement. (See
Chapter 5, "Getting Help," for
instructions.)
No. Call Dell for technical assistance. (See Chapter 5, "Getting Help," for
instructions.)

NOPE Not the solution, as this doesn't work any more either. It will go for a half a day not working, then start working. It will also go into hibernation or standby (slow glow-fadeout cycle) when lid is closed, no response touching on anything. all settings are set to off when lid is closed and everthing else is set to always on. To me, this seems like a software or BIOS issue...

I have the same problem...Pop off the little cover where the power switch is. Look at where the AC adapter is plugged in. gently tug on adapter. The AC connection to the board is probably broke like mine.