Chromecast devices are optimized to work best with specific Wi-Fi standards depending on where they are sold. This means if you buy a product in one country, it may not work as expected, or may not work at all, if you try to use it in a different country than where it was purchased. Sounds like whoever you bought the device from lives in a different country to yourself.
The first thing to try is to factory reset and retry setup. If that doesn’t resolve the issue, there are some workarounds you can try:
- If your router is a dual band router and has different network names for the two Wifi bands, try connecting to each band and retry setup.
- Login to the admin page of your router (refer to the manual or the back of the device).
- Navigate to Wifi or Wireless settings (the naming of the menu options you see will differ by router manufacturer and you may need to click to go into "advanced" settings to see some options).
- If your router is a dual band router and doesn't currently have different names for the two bands, look for an option to turn on different network names for the two bands.
- If "Wifi Protected Setup" or "WPS" is enabled, disable it.
- Set your Wifi channel/band (channel selection) to a value between 1 and 10.
As for power, it comes with the power adapter and cable you need. HDMI is a display technology, and can't be used for power. Like many electronics, Chromecast will get slightly warm during use, but it should not be too hot to touch.
