Hi Kerri! To recap what you've stated so far (making sure that I am on the same page as you): your computer battery fully discharged, and will not charge back up. Your laptop will not power on whether or not plugged in, and whether or not the battery is installed. Is that correct?
Assuming I'not not misunderstood, we are left with three potential causes of this problem: 1) a faulty power source, 2) a faulty power adapter, or 3) a failed mainboard inside your laptop.
We can rule out #1 pretty easily: try to plug your laptop into a different power outlet, and see if it will now boot. If it still does not boot, we know that a "faulty power source" is not to blame.
The other two issues are going to be a little trickier to test, because it will require you to have access to a new power adapter for your laptop. Compatible third-party power adapters can be purchased for about $60 from many electronics or office supply stores, and I recommend buying one locally -- so that you can more easily return it if you rule out the issue as being related to a faulty power adapter. At any rate, once you've acquired one please try to plug it into your laptop and see if your computer will now power on.
If your computer *still* will not power on, it would indicate that your computer is experiencing an electrical issue that should be repaired by a qualified technician.
If you have any additional questions, please let me know!