How do I promote a newly created social network for seriously ill medical patients, without "spamming" anyone?

[Vitaliteas]

Write a couple articles about the service, tell stories of how it is helping people or creating a community. Then post your article both on your site, and on Digg.com. The more votes it gets on Digg, the more people will see it.
http://www.digg.com

You could also advertise on StumbleUpon - it costs $0.05/click, and you can target your campaign to show to people who are similar to your targeted social group.
http://www.stumbleupon.com/ads/

I'd really think hard about keeping the Google ads on your site. Most people's perception is that you're making money from them (which your web hosting company is doing), and it sounds like that conflicts with the purpose of your site.

The ads also cheapen the look and feel of the site if not done well.