Normally, Homey always stays online and active in your account, so you can access it anywhere, anytime, by loggin in in your account. When your Homey turns up grey/inactive (and non-clickable) in your account, something might be off. This is what to do.
Make sure Homey is connected with the original adapter and cable to a power outlet, and that the power outlet does indeed provide power.
Check what Homey's LED ring does and tries to show you:
Make sure that your WiFi network is up, and your network is connected to the internet. You can check this by connecting to the WiFi network Homey is linked to with your mobile phone and see if your are able to load a webpage.
If after the previous steps Homey is still not online, you can initiate a reboot of Homey. To do this, unplug the adapter from the wall socket, wait 10 seconds and plug it back in. Homey wil now boot (with an orange loading animation) in a few minutes.
If, with a reboot and verified working WiFi network, Homey does not connect to the internet, place it in recovery mode and relink it to your network.