Dell Inspiron 8500 won't turn on

My old Dell Inspiron 8500 won't turn on.  I own two batteries for it, both of which can hold no charge (I have one of them inserted anyway).  When I first plug in the AC adapter, the battery light on the hinge illuminates in green for about 10 seconds, then flashes orange indefinitely.  When I push the power button, the power light on the hinge comes on, but nothing appears on the display.  The Caps Lock, Num Lock, and Scroll Lock lights all illuminate for less than a second, then the Caps Lock light flashes 9 times.  The Caps Lock and power lights then go out, and the laptop is off.

Here is a video of me attempting to boot up my laptop.

I've read that this problem can be resolved by removing one of the memory modules or making sure that both modules are properly seated.  I tried removing one memory module and had the same problem.  I put that memory module back in and removed the other memory module, and had the same problem.  I removed both memory modules, reinserted them, jiggled them around a bit to make sure they were properly seated before latching them in, and had the same problem.

Does anyone have any idea what may be wrong with my laptop, or how I might be able to resolve this issue?  Thanks!