Welcome!
If you have a hard disk, you should hear it spinning away inside the A1200. Additionally if it is *installed correctly and working*, as soon as the A1200 is powered on, it should start to load. The hard drive light will flicker on/off as it accesses the hard disk.
To check memory, load the Workbench disk and look at the title bar- standard Amiga 1200's have 2MB graphics memory and no Fast Memory (other memory).