Wait, does this site not have reply buttons? :-|. OK, one at a time then:
@Keng: that doesn't look like it would work; as far as I can tell blat is just a utility for sending mail through preexisting servers/accounts.
@aku: So, where do I get this magical "some.smtp.server"?
@Matt, @Biri: I agree a web service would be optimal; however, I'm kind of trying to host this program off of a free GooglePages account, which obviously doesn't allow such things. It would also be nice if my code was reusable by other hobbyists who probably don't have access to a setup.
@Matt: Regarding having the user enter their stuff, that seems like an unnecessary burden on the user, and would discourage sending error reports. And this is a Windows program, so no sendmail, sadly.
@Espo: that looks just about perfect! I did not know that would work! I guess it's a bit situational, but it works for my program!
@Chris: I'm not quite sure how to interpret your first sentence. I'm not trying to prevent others from sending email (or, say, spoofing error reports); I'm trying to prevent them from taking over the account and locking me out of it.
The idea of a webform makes some sense, but seems like a bit of a hack, and runs into the same problems as a webservice.
All in all, thanks everyone! That was an amazingly quick series of responses, almost all of which were quite helpful and a few of which even worked inside the limitations I failed to outline in the original question!