Thank you for responding. The problem with trying those is that my launcher doesn't work properly to begin with. The only way I can play the game when there's a patch is to have my husband patch his game, and then I copy his game over to my computer. Regardless, I went ahead and tried the repair. I don't have a bitraider folder (though I do have a brwc_swtor application, I don't know if that's something different or the same thing...), and I deleted the diskcachearena. Still just an empty mail and still no droid.
On a whim, I decided to try logging into the game on my husband's computer, and lo and behold, the mail with the M4-16 droid attachment worked on my characters there. It showed the text and the attachment and I was able to get it on all my characters minus my main character, which was the one I had initially tried to get the droid attachment from the blank mail I had first received on my computer, and tried the 'Get All Checked Message Attachments' button, which made the icon showing it had an attachment go away yet still a blank mail and no droid. So now, on that character on my husband's computer, it shows the mail like all my other characters there with all the text saying Here's Your May 4th Droid! but still no droid attachment..... So I went and got the droid pet on all my other characters, and went back on my main character and spent 1 cartel coin to get it out of collections, and finally my main character (the one I actually want it on) had gotten the M4-16 droid pet.
So after all that, I went back on my computer and logged in. And no droid. No droid on ANY of my characters. The mail still shows blank, there is no droid in any inventory or pet ability list on any of my characters, and my collections doesn't even show it exists. So now I'm completely at a loss as to why it works and shows on my husband's computer for my account, but when I log in on my computer, suddenly it acts like it doesn't even exist anymore. Clearly there is something going wrong between the game and my computer specifically and I haven't the slightest clue what that could be, as I have tried everything I could think of in the past to fix the previously mentioned issue I have with my launcher not working when there's a patch and the only fix we could find was copying my husband's copy of the patched game over to my computer.
Right now I am going to attempt to uninstall and reinstall the game (despite that NOT working in the past to fix my launcher issue) and if that doesn't work, will try to copy the husband's game over again.... Short of that, I don't know what else to do..... And it really irks me that non-subscribers/preferred players like myself can't actually get any direct help from the game developers themselves when issues like this come up that make us completely helpless to do anything about it, and it makes this game very undesirable to want to play (which irks me even further because I am a HUGE Star Wars fan and WANT to love and play this game....)