Here are the troubleshooting steps:
1. Ensure all of your physical connections are secured. Even if you think they are, try giving them a firm push into their sockets. Ensure the data cable going from the modem into the router are firmly into the ports of both devices. After doing so, wait a few minutes and check to see if you have internet connectivity again.
2. If step 1 doesn't work, and you've power cycled the devices as you've mentioned above, then unplug the data cable from your router and plug it directly into your laptop. So, you'll have the data cable connected from the modem directly into your router. Wait about 60 seconds and then see if you have internet access (go to google). If that works, try a website you haven't been to for awhile and ensure that works as well. If that does not work, your issue is with the modem and you'll need to contact your ISP, who will help you further.
3. If you do have internet connectivity directly connected to your modem in step 2, then the issue is likely with your router and is likely the result of a misconfiguration which only became apparent when your desktop died (which is odd, and I'd have to think further as to why that'd cause that). If you know your router's IP address, you'll need to access your router by entering the IP address into your web browser's address bar (e.g. http://192.168.0.254). That will bring you to the router's configuration GUI, where can check the settings and confirm what's going on.
I can give you more guidance once you've tried these steps.