MacMail jammed up - will not time out

Question

Email crisis, first time problem. My hardware and software are old and my internet connection is slow, so I know there's not much horsepower here. Also, my emailboxes require severe spring cleaning and I should've known better than attempt to compose an email (saved as a Draft, that's when problem occurred) with such a hefty attachment. I had to get out by using Force Quit.
Nonetheless, that having been said, when I try to open Mail the window immediately shows the Drafts mailbox with the endless spinning wheel suggesting an operation is in process - - this will go on forever, the computer seems to be gagging on the Draft I tried to save. Even when I am able to see Activity Viewer, my attempts to stop the listed operations are unsuccessful. I have taken the computer offline to try to let the program time out (wheel stop spinning) for up to 36 hours. Doing this, eventually the window will show all the Drafts in the mailbox but the wheel continues to spin thus the appliction allows no other action to take place.
What I want to be able to do is clear up this mess I've made, delete all unnecessary email sitting in various mailboxes, and get the program to respond again.

Answer 1

Well, after 11 days of frustration, I seemed to have fixed this dilemma with lots of trial and error, many, many restarts and very long waits, and applying every variation of the multiple tips posted herein from the various patient and knowledgeable global assistants participating on this site. Thanks so much to all.
During this final push to conquer, after waiting 40+ hours for Mail to timeout, I felt like I almost made a mistake to set me back to square one but somehow averted disaster. With Activity Viewer finally showing that "updating color" for all 16 messages had completed, I mistakenly Forced Quit and thought I might lose all this progress. However, with this activity finally having timed out, along with having moved the Drafts .mbox out of the HD Mail folder onto desktop, Mail re-opened easily and then I was able to finally access and view the Drafts mailbox listing all 16 messages and their size - - - and with no spinning beachball! Very tentatively, I clicked on the largest message and hallelujah - - - again no beachball! I immediately proceeded to slowly and carefully delete each of these Draft messages, then delete all Mail trash, and begin house cleaning all of these folders in Mail.
It has taken a few other steps to get this machine back to normal. When I re-started computer, Mail proceeded to load 502 duplicate incoming messages, which I just waited out and then deleted without opening. Lastly, the first few times I tried to shut down the computer using Shut Down from pulldown Apple menu, the Shut Down button in the follow-up window did not respond. The first time I used the old paperclip emergency restart; the next time I was able to shut down using keyboard on-off. Third or fourth time and the usual Apple pulldown menu functioned just fine.
It has only been a day so far, but it appears that things are running reasonably well again. I will continue to clean-up and remove useless data of all types (now and in the future) to allow this machine a little more latitude to perform its called-upon functions. Also, I shall soon learn how to post responsive and appropriate ratings on this site for all of you who helped me work thru this mess.
I will probably be keeping this computer active for at least several more months, but intend to eventually upgrade to a used G5 iMac, probably an earlier generation. Any final tips from you helpful folks would be appreciated regarding:
A. Any simple, routine maintenance operations on this current G3 iMac?
B. Any particular G5 iMac models to pursue or avoid?
Thanks so much again for your patience and sharing your knowledge. This is truly a helpful discussion site.
Robert