If you really think about it, what can you provide thats unique to your target market. If that is sufficient enough, then start from there, and whatever else you will need look at other people you know are trustworthy and see if they fit your criteria. If that doesn't work as people above have said linkedin can be a good resource, but not your only option. Maybe start yourself, and after networking a little bit in your area, you will find that unique person that stands out, who could invest in your company and be even better than your original partner.
That's a tricky question to answer without knowing the business you're going into or the skills of you and your former partner.
Is there anyone your former partner could recommend? If you have extensive connections on LinkedIn or Twitter, try asking them for recommendations.
--- Online business ideas, resources and strategies for a profitable website.
In my opinion, the best solution is to think about new idea because I don't think you would find in linkedin someone trustworthy :) or just live your life and you'll meet a proper person during your career/job practise.
Honestly, if the business depended on having both of you and they left before you really got started -- I think that you should just consider starting a different business.
If that's not an option for you, then try to outsource the responsibilities that your cofounder would have had until you're able to do it yourself.
I'd be hesitant about finding someone online to start a business with -- having a cofounder is an intense thing, like a marriage, and I wouldn't enter into either partnership lightly.
---How much would liability insurance cost for your startup or small business?
LinkedIn is a great resource as many people have recommendations on their profiles. Have you spread the word in your networks so you can solicit referrals? What about networking in person, in your industry, or wherever you might find that skill set, to meet new people? I think nothing compares to interacting with someone in person. Then you will have to trust your instincts. Also, make sure you speak to a business attorney about all the possibilities if you "break up."
My business partner and I were starting a unique consulting business where both of our skills combined is what made the service unique. He found that after a few weeks in the planning stage that he didnt have the time needed to proceed further.
Question - how do I find someone trustworthy/dependable, etc that I can replace him with?
Getting others who have the same vision is tough. It seems that with a little success, others are more likely to want to join and be committed. It's sad, but that's just the way it is. As mentioned above, I'd go with trying to start on your own with what you can and grow from there.