1992 Ford Tempo wont start

When you say no noise when you try top start it do you mean dash warning lights come on but starter makes no noise? And there is no hum from back seat of fuel pump running?

The fuel pump is right under back seat middle and makes a hum whirr noise for a couple secs if you just turn key to dash warning lights on. Of course if you turn key all the way starter is supposed to engage and grind as you say? Also some under dash relays may make ckick sound. Starter relay under hood makes fairly loud click also. But you dont hear click when starter works properly.
Your starter relay is under hood on top of drivers inner fender wall. The small wire with rubber boot is from your ignition switch. You can unplug and run another wire from hot on battery to this post and toouch and starter should grind away. If not you will at least hear a loud click as this selenoid clamps. If no click make sure 2 small base attachment mount screws to fender wall are clean and tight. If still no click it's bad. If click but no start then starter is suspect. Brushes are probably worn and causing intermittent/unreliable contact. If it works out there but not in car with key then ignition switch/wire is suspect. You should also first make sure battery posts connections are clean/shiny and tight. They can either be powdery/chalky when bad or just have a black coating that blocks good contact.