There are a lot of questions here.
1. What happens when you connect the computer directly to the modem after a reset?
Does the connection to the Internet refresh quicker?
2. What area the IP addresses of the modem and D-Link after the reset?
3. Has the modem been bridged?
4. How is the D-Link configures to receive an IP address?
5. Have you tried renewing the computer IP address using these commands in a Command Prompt Window?