All that "non-profit" means is, from Wikipedia, :
"A non-profit organization is an organization that uses its surplus revenues to further achieve its purpose or mission, rather than distributing its surplus income to the organization's shareholders (or equivalents) as profit or dividends."
There are plenty of ways to raise capital that allow an organization to abide by such restrictions. A nonprofit is not strictly restricted on who it can hire or what products it can make or services it can offer. So, unless your definition of "successful" requires that you distribute surplus revenues to shareholders, then yes, it is possible to start a successful tech non-profit.
You can pay your employees massive salaries. You can raise massive amounts of debt to fund your expansion. You can employ ruthless business practices.
Many businesses do not distribute capital to shareholders until well after the business has matured, reasoning that the capital is better used growing the business. Meaning, the investors have a long investment horizon. Meaning, their initial smaller amount, often accompanied by additional rounds of funding, was enough to get a successful business going. Capital sources can include endowments, public and private grants, or payment for goods and services.
Personally, I believe that non-profits have gotten a bad wrap. There are some amazing companies out there that do not aim to return money to shareholders, that prioritize their product, their cause, or their customers. I'd highly, highly recommend checking out YouTube videos about Patagonia and it's founder, along these lines. You can even mis-use non-profit status. Many people don't realize that IKEA is a non-profit, and that the profits are extracted from its activities through some tax and legal loopholes.
Typically, the relevant issues are related to the raising of capital. But think about how that often turns out. Many founders raising outside capital lose control of their company or see their share diluted, that is if the company is even successful. And if it is, and they maintain control and their share of ownership, it could be a long time before there is any surplus revenue.
On the flip side, you can start a private company and be help accountable to no one but yourself. You can raise all different sorts of capital. And you can determine what social / environmental impact you make. You pretty much only lose the tax breaks.
So you see, it's really a matter of capital management, not of business management. You can reduce your options for raising capital from the get go, or you can choose to deal with taxes and possibly even make those go away, like GE magically does. But there are no impediments to you delivering a product or service to make the sort of impact you are hoping to make.