It absolutely IS your responsibility for you do a trademark search before you sell a domain name. Otherwise you could be selling someone else trademark property which you have no right to do. Leading to lawsuits and a damaged reputation. Research before you claim and sell and domain.

By learning how to be resourceful. Getting the money you need from the people who have it. Take a current look at your assets and if you can use them to secure funds. Look at your network is there people who may be interested in investing. Bootstrap, start a kickstarter, low interest business loan, competitions, get your early
adopters to pay prior to receiving your product.
Resourcefulness is a key factor to getting more money.

As a startup a SWOT analysis is a very important part of your business plan that should be conducted on both Yourself and Your Co - founder/ business partners as well as the actual business itself. You want to know if you yourself and co founder have the Entrepreneurial Mindset necessary to start and run a business for the long term. You want to know what skills and resources you bring or need to acquire for the success of your business. You want to do a SWOT analysis on your business during your pro-type launch stage to learn what your target audience think about your product/service. And every stage there after. So in short a start up should have already thought about their SWOT analysis on themselves as owners prior to launching. A SWOT at pro-type launch and another SWOT analysis after using the feedback from pro-type launch to improve and every 6months their after to remain aware of any opportunities and needs
for improvements.