First off, I'm not a wrench, so my knowledge and experience is severely limited; I'm not even sure which part I'm looking at, or if it is the problem. Please bear with me.
Here's a little history of the problem. I noticed a clicking sound under the hood that came on when I turned the key to start the engine. It didn't happen every time, and it usually subsided after the engine had run for a couple of minutes. Also, it would stop completely when I stepped on the brake pedal, but would resume as soon as I let off. When I took it to the shop for the timing belt/water pump maintenance, I told them about it, but as I said, it didn't happen all the time. It didn't happen while they had it, so, it wasn't fixed. I guess they thought I was crazy.
Recently, I pulled into a gas station and parked facing slightly uphill. When I came back out, car wouldn't start. I pushed it to one of the pumps where it'd be level so I could check fuses & fluids, etc, and it started right up. I have no idea if it being level has anything to do with it, but I figured I'd throw in every detail I could remember. A couple of days later it died on me again while on the highway....I coasted to a safe turnoff, waited a couple minutes, and it started again. A week later it happened again, this time a stone's throw away from my house. I walked home, and came back a half hour later, and it started up. I got to my driveway, and it died, so I coasted in. It wouldn't start again for two weeks. It would turn over, but not catch. I put some 'Sea Foam' in the gas tank. When I tried to start it again a couple of days later, it started, and ran fine for a week. Now, it won't start again.
Poking around under the hood, the below pictured component is making a hissing, sometimes popping electrical sound when the key is turned to the 'on' position. This is also the thing that's making the intermittent clicking sound.
So, what am I looking at here? Any diagnoses/help? Thanks in advance.