Accounts can be setup with an ISP to get an IP address using different methods. But, almost certainly, yours is setup to use a protocol called DHCP where your computer requests an IP address from your ISP. Your ISP sends you a "lease" on an IP address. (it;s a lease cause ur ISP can terminate the lease and change it on you! but, you, the user should never know the difference)
Your problem indicates you can't communicate properly with your ISP.
Go ahead and post your configuration but use the /all parameter:
ipconfig /all
Most likely, though, you have a connection problem with your ISP. In fact, the new modem may have added to the problem as you may need to register it's MAC address with your ISP before they start talking to it. (The MAC address is probably printed on a sticker on our modem. )
Call them