Thank you very much for all of your help, Howie!Last option - and it's a bit drastic.
I found that video you reference. It doesn't look too bad... but is a pain. If you go that route be careful with the ribbon connectors as they can be damaged easily if pulled in the wrong direction. Some have a metal lock plate that keeps them in place. Those usually lift slightly to allow the ribbon to be pulled out. You'll also want a spludger (basically a thin metal or plastic flat blade that's used to pry apart the case to pop those friction tabs open without damaging the case or tabs) to help with case disassembly.
Rather than attempting to remove the BIOS battery you might be able to locate and "short" across the CMOS reset jumper pads. This diagram is one I found for the E1-521 model but yours should be similar. The jumper connections are under the RAM, which you'll have to remove to access. Use some hemostats or needle nose pliers to short across the connections and then press the power button. It only takes a couple of seconds following turning the system on for the CMOS to clear using this method. Do not let the pliers touch any connections other than the 2 CMOS pads. If your system doesn't have the pads labeled as CMOS (like in this image) or the location is vague then just don't experiment as you can ruin the motherboard if you short the wrong pins. This will have the same effect as removing the CMOS battery.
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Unfortunately though, I think that even removing the ram in my Acer Laptop might be a bit more than I'm comfortable with, never mind tinkering with jumper connections on the motherboard. If this were a tower instead of a Laptop, it would be a different story, as I'd have no problem with CMOS Battery removal on that type of setup.
As it stands, a local brick and mortar electronics merchant just gave me a $45 - $55 estimate over the phone, for resetting the BIOS. I'll be calling back Wednesday after he checks with his technician regarding possible trade for my WD 320 GB External HD. I really want to bring my Acer Aspire E1-522 Laptop back from its current useless state, if at all possible.