Accord LX Manual has trouble starting

My 94 Accord LX Manual transmission is sporadic in its starting.

I turn the key, whether with the clutch in or out, it SOMETIMES clicks
twice,
like from the inside of a tin can (tink..TINK, or click..CLICK).
Nothing.

Ill do it a few more times and turn the ignition off, pull the key
out, and
sometimes that helps. I thought I had it licked when I had the shop
tighten
up the VERY loose battery leads. They were almost falling off! I
dont know
how the car even started...they were THAT loose. A bump could have
tossed them
off the terminals. I had the battery checked (by the guys who sold it
to me, dumb) and they said the core was fine.

Sometimes, after driving for a bit, the car will be fine. Other
times, it is a stubborn old mule and wont start. Bump starting it
always works, and easily.
It takes about a foot to bump start her.

I was told it might be the ignition switch, but why the mechanical
click-click?

Also, I was told it might be a relay, but would it click if the relay
was
faulty?

A more trusted source says the contacts on the starter (solenoid??) is
likely
crusty with corrosion or something, and the whole starter should be
pulled
(because the contacts supposedly on the 94 accord manual cannot be
independently replaced??)

HELP!!