A client is not responding?
We get paid automatically if clients don't respond.
So unless you, as the freelancer, made a mistake, this is a non-issue.
Is this a fixed-price contract with a fully funded milestone, and you submitted your work using the official green Submit Work / Request Payment button?
Is this an hourly contract and you logged your time?
If you can answer yes to one of these questions, then relax. You will be paid.
If you answer no to both questions, then you made a mistake. You need to learn how to use Upwork properly. Provide us with more details and we will tell you what to do next.
re: "I have sent him an invoice for the work (the work was an hourly paid contract with payment verified), but he hasn't replied to me since that time. that was about 2 weeks ago."
We don't "send invoices."
It sounds like you don't know how to use Upwork properly. You don't need to wait two weeks to see your earnings. The money you earn shows up on your Reports screen WITHIN THIRTY MINUTES of when you do the work. The money would already be in your bank account if you did this correctly.
Go to the Upwork help section and read about getting paid. If you used the system correctly, there is no need to communicate with the client. Either your hourly work is paid automatically or you should have submitted a request (once) for any fixed price work. Once a project is completed, there's really no reason for the client to communicate unless they want to work with you again. You will appear unprofessional if you are asking someone to pay you without knowing how to get paid. So-- go do your reading and learn so that you can present yourself well to clients.