Fangly

Hi! This is my first post, so bear with me! I own a 2001 Impala base 3.4L that I purchased to fix up for resale. Unfortunately, over the winter I let the battery run down, and when I tried to charge it up, it wouldn't hold a charge, so I replaced it. Now I'm hostage to the security system. I insert the key, the cluster lights up, but no crank. The red light on the radio is flashing, and I get assorted messages on the display. I've looked at various information online and this is what I have tried: pulling the BCM fuse repeatedly; no luck. Leaving the key in the On position for more than 10 minutes (the red light on the radio never goes steady); no luck. I cannot get into the menu on the radio; it shows the time and then nothing. The car is in a dry and tight storage unit, so no moisture/weather damage. I have trouble believing that the BCM is bad; everything was working just fine before I let the battery run down. Never a problem in starting the car previously, so I'm at my wit's end. I really don't want to have the car towed to the dealer for them to charge me mucho bucks for a (hopefully!) simple fix. I know other models have had this same problem, so that is why I posted in this forum versus the Impala one. Does anyone have a solution before I wash my hands of this crate, and have it towed off to the junkyard? Thanks in advance!!