1994 Toyota Camry Start issues

About a week ago my 4cyl. Camry did not want to start on the first or second try. All I would hear was a single click every time I tried. I proceeded to check the fuses and they all checked out fine. So I wiggled a couple of relay boxes in the engine compartment sat back in the car, gave it another shot and it started right up. I didn't have this problem for about a week or so. Then two days ago it just wouldn't start period. Tried wiggling the relay boxes, nothing worked. So I had the car towed and my starter was replaced. Today I got off work picked the car up and it started right up. I got home took a nap and then decided to go grab some dinner. I jumped in the car and crap, it wouldn't start again. This time I noticed there wasn't an open door chime with the key in the ignition and my door locks weren't working. I grabbed my owners manual and noticed that three relays in the instrument panel were actually replaced by a part labeled "Relay Integration" module, this Relay Integration module controls my starter and my power windows, power door locks, rear window defroster. I'm wondering if this is the faulty part? I'm inclined to say so but I don't want to waste my $ just replacing parts. Does anyone have any clue what other issue could be responsible? BTW, my battery and alternator are working just fine.

Many thanks in advance!

Anone? Any clues as to what might be causing this issue?

Get a wiring diagram and start checking circuits for opens, grounds, broken or frayed wires, etc.

Where can I get a wiring diagram from?

There are a number of places:

You could get a subscription to alldata.com

Buy a service manual

Maybe your local public library might have the manual.