There could be several reasons why your Apple Mac is not connecting to your broadband network. Here are a few troubleshooting steps you can follow:
1. **Check your Wi-Fi settings**: Ensure your Wi-Fi is turned on. Click on the Wi-Fi icon at the top of the screen and make sure it's switched on. If it's off, switch it on and try to connect again.
2. **Check your network**: Make sure that your broadband network is working properly. You can do this by connecting another device to the network. If other devices can connect, then the issue is likely with your Mac. If no devices can connect, the problem might be with your network or router.
3. **Restart your router**: Sometimes, a simple restart can solve the problem. Unplug your router, wait for about a minute, then plug it back in. Wait for the router to fully boot up, then try to connect your Mac again.
4. **Forget the network and reconnect**: Go to System Preferences > Network > Wi-Fi > Advanced, then select your network and click the minus (-) button to remove it. Then try to reconnect to the network.
5. **Check your DNS settings**: Incorrect DNS settings can prevent your Mac from connecting to the internet. Go to System Preferences > Network > Advanced > DNS and make sure your DNS settings are correct. If you're unsure, you can use Google's public DNS (8.8.8.8 and 8.8.4.4).
6. **Update your Mac**: Make sure your Mac is up to date. Go to the Apple menu > About This Mac > Software Update to check for updates. If there's an update available, install it.
7. **Contact your ISP**: If none of the above solutions work, there might be an issue with your Internet Service Provider. Contact them for further assistance.
Remember, it's important to keep your devices and network secure. Always use a strong, unique password for your Wi-Fi network, and regularly update your devices to protect against potential security threats.