Failing to turn on when I turn the key in the ignition

Hello, I have a 98 Saturn SW2 that has recently been failing to turn on when I turn the key in the ignition. It comes and goes. Also, there is no clicking noise whatsoever. The lights/radio come on, but no noise.

When it happened the other day, I took it in to see if a lube place could assess what was wrong. They quickly noticed that both battery wires were loose--especially the positive wire.

After they tightened these, I turned my car on and off several times to see if there were any changes. It started up just fine each time, so I assumed the loose wires had caused the random dead car scenario.

Then just yesterday, I drove my car with no problems in the morning. I go to start it only forty-five minutes later, and it's dead again.I'm starting to worry and think it's the starter, but I also think maybe the wiring needs to be tightened, cleaned, or replaced.

Any ideas?