I have two problems, that I'm not really sure how to fix.  So I thought I might try asking for help here.

The FIRST, is that whenever I remove my AC adapter, the laptop locks up in it's entirety and regardless of time passing won't respond. 

The SECOND, is that when I wake my computer up from standby/hibernation and occasinally when I open my laptop after closing it, the screen will be black, with only the cursor visible.  To remedy this, if I'm waking up from standby/hibernation, I just have to move my cursor around until it turns into the "I" figure, and type my password.  If I'm opening my laptop, I just have to ctrl+alt+del and hit cancel (or do anything else, for that matter). 

Any IDEAS on how to fix EITHER of these problems?It's a longshot, but download and install the latest chipset drivers for your laptop.  Hopefully, that will resolve the hibernation/general power issues.

Alternatively, you could try flashing the BIOS, but that seems pretty risky at this point (especially if your laptop freezes during the flash...you'll have an expensive brick...). 

Another thing you might want to look at is whether or not the battery is on the verge of death.  Sometimes a dying battery can do more to a laptop than just turn the thing off if it has no AC power.  I've seen anywhere from BSODs to frozen splash screen boots (yes, I know, "What are you smoking, B?"...but seriously, it can happen).  Another alternative, although this more involved is to start from scratch and back up the HDD files and do a clean install of the operating system.

 I just noticed that you have what i said as your signature, i remember posting that, i was right BTW i got the computer back about two months later and was asked to format it due to viruses.