Problem 2: Security
Remember when we were all sophomores and Rob hacked into everyone's email accounts and registered with hundreds of fetish porn sites and then we were inundated with amputee erotica and we thought it was a pretty good prank but then Rob ended up leaving school for that sex addict rehabilitation center in Oregon? I think we all learned a valuable lesson that year: Your security was terrible. Rob was not a genius; his crowning achievement of technological wizardry was memorizing cheat codes for SimAnt. He hacked into our email just by testing the password "eh" and it worked... on every account. You were responsible for what is still considered, the most widespread security incident in the history of the Web.
The only amputee erotica picture I kept.
Problem 3: Spam
Your spam filters are lazy. The open door policy you allow for junk mail is absurd. I get eight emails a day offering to make me a registered nurse in only six weeks. And just so we're on the same page, Hotmail, I would be a terrible goddamn nurse; I don't like blood, old people or florescent lighting. Also, I'm pretty sure an RN needs at least three years of schooling.
A finger painting I did of nurses getting schooled.
And these are just the three most egregious of your problems, but I have a solution that requires fixing none of them. There is a simple way for you to become a popular and usable Internet provider again with only some careful re-branding, and an honest look at yourself. I would have written this suggestion to your technical support but you don't have one. In fact, you might be the only email service without its own easily accessible email account. You are rich with disappointment.
Rather than try to catch up with Yahoo! Mail, Gmail and... ugh, AOL, you need to redefine the expectations of your users. Don't hide your flaws, use them to your advantage. You can be:
Hotmail: The Garbage Man of the Internet
Unlike real garbage men, you won't encounter dead bodies like this one.