After a bit of investigation, I think the problem may be the "word verification" feature -- if you are unfamiliar with how this works and why it is there, it is easy to miss! If you are trying to leave a comment but do not have a Blogger account, you may choose to comment as "Name/URL" from the drop down menu. (A URL is basically a web address -- if you do not have a personal website, just leave that field blank.) Once you hit "Post Comment," you will be asked to verify that you are not a spambot by re-typing a randomly generated "word" image, like the one below:
In this case, you would type "twartme" into the blank field before hitting the "Post Comment" button for the final time. The verification "word" changes at random, and appears "wavy," to fool spambots -- it is easier for an intelligent human to discern letters, despite any distortions, than an automatic script.
(The "handicapped" symbol next to the blank field is for those who are vision-impaired or cannot discern the verification word. Instead, by clicking on the symbol, you will listen to a series of numbers read aloud against a background of "gibberish" and type the numbers you hear.)
In my mom's case, she was using Internet Explorer and the word verification feature was not even loading. My husband fixed this by going to Tools --> Internet Options --> Content --> Clear SSL State. Why that worked is beyond my Internet knowledge. ;-) So if your problem is like my mom's and you're not even seeing the word verification option, consult your nearest computer nerd. :-)
That wraps up my little tutorial! I hope it helps anyone who's been having troubles leaving comments.