What internet/technology startups have attempted to solve "hard problems in computer science?"

Not to be lazy, but: Google.  Doing indexing and search correctly over the entire public internet is hard and they've done a good job of solving many related problems (including during the time period when it could safely be called a startup).

Google is generally thought to be a fairly successful company.

How much equity should I expect when joining a company of two people as an employee, when the company is roughly one year old?

Consultancy is not a scalable business, not high growth business than can have significant ROI. Consultants bill for their time, no one has been able to stretch a day beyond 24 hours.
Why are you taking 50% salary cut? To do new product development for your consultant friends? It doesn't sound to me like they have significant skin in the game, they want you to get a salary cut and then some one will magically come up with a new product that, if you are lucky will be profitable.

How are small development teams normally structured at startups?

I'd agree with what Justin says; startups around software are typically badly structured. However, in the ones that I've been involved in (both as a developer, and as the lead technical role) there has been some formal structure – although unlikely to be on paper!
 
Typically there was:
 
Lead Developer
The lead developer was responsible for a lot of the technical design work that went into the project, as well as crafting the original code, conducting reviews, ensuring it was compliant with any policies (always have a coding standard in place even on startups!) etc
 
Developer(s)
Usually one, junior, developer to start, with but grew as needed.
 
Testing usually fell down to the developers, or another stakeholder – i.e. anyone available. I've never seen startups have the funding for a nice clearly defined testing role, or even a support role until after public launch of a product!
Only one startup that I have been involved in had a UX person on board, and that was well after initial prototypes, demos and funding rounds were completed; before that, it was all guess work and a little outsourced.

How does 280 North plan to make money?

Selling software, probably as a service.

From this blog post, it sounds like they do plan on selling Atlas.
http://280.posterous.com/announc…

"The Atlas Developer Beta Program will have a $20 membership fee, and will launch on November 15th. To be clear, the beta program is separate from the final version, and the price does not reflect the final Atlas price."

Other than employing a large sales force what are the most effective B2B customer acquisition tactics that a startup has used?

Channel Strategy. Big companies don't typically make money by building innovative new products, they let start-ups take that risk. They buy or white label innovative new products. Find big companies, integrators, VARs, or OEMs, and build a partnership. If your VP of Marketing doesn't have experience doing this, try asking your investors or founder network for introductions and some help in the early meetings. In these deals, knowing how to put the deal together is more important than the pitch.

What are the best examples of start-ups that have financed fast growth through negative working capital?

Thanks for the A2A.

Financing growth through negative working capital is a tough job.

Amazon has been able to do it successfully, but typically even if a company has negative working capital requirement because of high cost of customer acquisition they require funding to continue growth.

Subscription revenue based companies which are able to manage the customer acquisition cost would be an example of this.

Though not sure but by the look of it CB Insights driven by Anand Sanwal might be an example of growth driven by negative working capital.

Also though no longer a startup Airbnb (product) is also an example

My 2 cents…

​Mrinal|LinkedIn

Why is there not more innovation in the webmail space?

The question is very vague. Is the person talking about the past year or so? Is he talking about all systems (hotmail, gmail, yahoo mail)? Or is he only talking about webmail clients that you can host?

That said, I would actually submit that if you do a little thinking over the past five years that the email web clients have improved in many ways. Gmail is probably one of the largest proponents of change; seeing as its been around since 2004 in beta or 2007 for the public, it hasn't done have bad considering. Sure, the technology for transmission hasn't changed since the early 1990s. (By the way, Google Wave attempted to innovative in 2009 with the transmission, but it didn't catch on and died a little over a year later.)