These people are signing up, but when we send them an email to verify their email, they don’t do it. Either they don’t open the email or they open it and don’t click the link. When we send a reminder the same thing happens. What do you make of that and what should we do to get better follow through? Should we ignore these people or try harder to engage them?
Great question, but it's really hard to answer without knowing what service you provide. Also, it really depends what percentage your talking about - if its low - I wouldn't waste time on it for now.
I myself have personally wanted to use an online service which claimed to be free, and the sign-up deterred me so I just gave a wrong email address. If it's a once-off action on behalf of the user (for example converting a file), users are lazy and even something like giving their email deters them.
I am happy to solve this issue with you, but I would need to get more details, following which we could have a short call to discuss the conclusions.