http://kb.mozillazine.org/Moving_your_profile_folder_-_Thunderbird

I was able to copy Profiles folder to my desktop...I then opened that and found the Mail folder and opened that...then I opened drafts which had very strange titles or codes with the dates created....but how do I actually read one of my Drafts? Thanks. I am a novice at all of this.

I want to transfer my email drafts and my sent email messages to a new PC computer.

I'm not exactly sure what you're up to. Typically one would want to transfer the entire Thunderbird profile to the new computer. This is what you'll achieve when you follow the instructions in the article linked above.

About profiles, see https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data You can also follow the backup and 'restore to a different location' instructions in this article to move the profile to the new computer.

If you don't want to move the entire profile, but just mail in Drafts and Sent see http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Thunderbird#Mail