You are looking at the wrong screen of the G1000. Look at the left screen. There you see a compass rose with an arrow in it. If that arrow is magenta, you’re in GPS mode. Click the CDI button. It will turn green. That is what you need. A green arrow tells you you’re in NAV mode, needed for an ILS approach.
Don’t look at the magenta line on the right screen (MFD). Thats only the leg of the route you’re on. Has nothing to do with the ILS.
Did you do an ILS tutorial? You will be inspired.