There isn't a formally defined "startup funds" with a set, fixed meaning. You will have to examine your potential contributors individually, and see what their charter and their motives are.
That said, most startup funding will not be available to you. It often falls in one of two categories:
That said, there is a lot of crossover, and some people do a majority of their investment on a for-profit basis, but leave room for a few social entrepreneurship investments as well. So as said, you'll have to take each potential donor as he/she comes, and get to understand their motives, desires etc.
As long as you make it clear its for a new venture within the existing NPO and not money going to sustain the main venture I think you could contact investors or donors who are willing to donate money to startup the new arm. If you could incorporate it under a different name and make it in association with your larger company that could work as well. Perhaps as your larger current donors what they think.