1995 Ford F150 wont start, looking for advice

I have a vehicle which has been sitting for 2-3 years and ran perfect when I left it. I have replaced the battery and battery connectors because thought that might be part of the problem since even the ding would go in and it when the door was open or key in it.

Symptoms: After replacing the battery, and even before, when I put the key in and turn it, the radio lights up, I can see the mileage display but trying to start just produces a clicking noise. It's not a continuous noise either, usually just a "chk" kind of sound. Subsequent attempts do not light up the radio or mileage displays but the "chk" sound is still there. If I let it sit a bit and try to start again, I get the lights and everything like normal.

Spark plugs and the fuel pump were replaced 6 months or so before parking it. There is some evidence of mice under the hood so maybe something chewed?