The best thing to do to start any kind of sales or relationship building process with a Fortune 500 company is to recruit willing champions of you and your company.
The good thing about Fortune 500 companies is that there are *lots* of people who you can potentially recruit. Many of them are active on Twitter and LinkedIn.
I've successfully sold to Fortune 500 companies this way and I'd be happy to share relevant tips with you.
You can do a little research on LinkedIn or Jigsaw about the right person to speak with. That's pretty easy stuff.
To start -- keep it short. The key to getting the best response is to frame your question so that the other company understands the value in continuing the conversation with you.
BTW, use a tool like Yesware or Boomerang to remind you when you've sent an email that has not received a response yet.
p.s. Lots more to this discussion. But that should get you started.
Actually, old school custdev from Blank's 4 Steps to the Epiphany goes a long way here.
Take the time to identify and design your strategy for:
The challenging thing about the Fortune 500 is that you'll meet several people who have the power to say no, but not many who have the power to say yes.
To add to what Dan, David & Tom have already said:
1. know the history of the company
2. find out all current news regarding the company
3. identify a current problem they are facing, for which you have the solution.
4. identify the relevant person.
Then you can make your sales call.
Hope this helps