So, here's the sitch.

My 93 camry wagon just passed 140,000. It was running fine last Sunday, and then it sat in the garage forfour days before I used ita gain, at which point it would not start. Lights come on, cranks, doesn't turn over.

Consulting with both my dad and the web, we started running a few tests. Pulled out a sparkplug, stuck a screw driver in, cranked while bringing the screwdriver close to a ground... no spark. Next, we took off the distributor cap... some corrosion on the terminals, but checking the flow with an ohm meter confirmed it wasn't bad. Then we checked the primary and secondary terminals on the ignition coil.

With normal coils, it's supposed to read .05-.2 ohms on the primary, and 10-14k on the secondary. With dad's old meter, we got 0 on the first, and 4k on the second. Confusing readings, and the guys at the local parts store agreed. We bought a new ohm meter, and are going to try again, see if we just had a bad reading.

That said, we've also been told that there might be a fuel system problem, but we're having a hard time diagnosing what that sounds like... (being that we're supposed to listen for it while the key is turned to ON)

ANy help appreciated!

This is a 4 cyl, correct? If you want to 'listen' to the fuel pump, do this. Find the diagnostic check connector under the hood. Flip it open and jump termanals, FP and B+. Turn on the key and listen.
Probably OK.
My gut feeling is the ignition coil. Look for any cracks on front or hot spots near the dist shaft.
I've had many of these that read good in ohms, but a new one fixed the no start.
Get one from the dealer. Give them the P# right off the front of it. It's 93.00.
An aftermarket coil is never reliable IMO. It's also time for cap/rotor/wires, plugs, too.

I've already bought a new cap/rotor, but am waiting to replace just yet...

I finally found the Diagnostic check connector, but it's covered in earwaxy crap. Is this normal? And if not, could it be a symptom/cause of the problem?

What should I use to jump the terminals? (outside of my experience)

New ohm meter measures .8-.9 across the primary (normal) but still only 4.5k across secondary...

Replace the Ignition Control Module and coil. I recommend replacing them every 120,000 miles or 10 years, whichever comes first, in order to restore "like new" reliability and performance.

The earwaxy crap is just very old white connector grease. Just take a rag and swipe it off the top.
If you don't want to make your own jumper with 2 male pins, then I tell most just use a paper clip straightened out.