Most likely yea from what you are explaining if the other computer works then there shouldn't be a problem with your network.
Things you want to check before you go out and buy another network card:
Physical Layer Problems:
The Ethernet cable, sometime they do go bad, try using a known working one from another computer to test this.
The port on your switch or router, try another known working port.
Check to see if the network card is installed in the slot properly and is not loose, if the card is build-in, check BIOS or device manager to see if it's enable.
Reinstall or update driver if you have to.
Network Layer Problems:
Test the TCP/IP stack with the ping 127.0.0.1 command
Check IP configuration with ipconfig /all (verify configuration such as subnet, default gateway and DNS matches with other computer in the network)
Use ping to test connectivity to the router by pinging the default gateway, example command (ping 192.168.1.1)
Once verified that you can ping default gateway, use ping again to test DNS and Internet connectivity by pinging a website, example command (ping google.com)
Application Layer Problems:
Software firewall or Anti-virus can cause you to lose Internet connectivity, it is always wise to disable or configure them properly during the test.
Example of application layer problems are usually proxy servers, typically these are use to cache website or surf the web anonymously. Once a proxy server goes down, the web browser can no longer function properly but ping should be able to work. Only if you use transparent proxy which redirects all request on port 80 to a proxy server but the rest of the Internet traffic is direct connection. Typical setup for those who browse the web anonymously using free proxy server on the web.