Sounds like your starter is bad.

 

I had a similar issue before where the car got harder to start over time. I believe it ended up being the starter contacts going bad.

 

And it is an ordeal changing the starter. Have fun.

 

The solenoid contact in the starter wears out, but you can tale it apart an replace it. At toyota they have the copper contacts. I have also made them out of copper plumbing pipe hammered flat and trimmed to shape. The pipe copper is not as nice as the toyota copper though and only lasts about 40% as long.

 

The way to diagnose the "contacts" issue is this.
You will need a helper.

You DON'T want to R&R the starter if it's not required!
Please be sure that the battery connections are clean and tight.
Be sure that the fat wire to the starter is not damaged/corroded.
Reach up there and check the connection at the starter terminal.
Both wires.
Ensure that the starter mounting bolts are tight.
Engine ground wire connections.
If that is all good.......

Find a good place to get the car in the air so you can crawl underneath it safely.
I use a 2' hunk of re-bar,but a 1/2" ratchet extension works fine.
AS your helper turns the key to the START position,and holds it there,it clicks but the starter motor won't turn over the engine,
RAP the starter case with the re-bar/extension.
If the starter enguages at the time of the "RAP",you will be replacing the starter/contacts.

This method is 100% true to diagnose a bad starter.

2 things happen:
It jars the starter assembly enough to change the contact area in the solenoid,AND/OR
It causes a slight movement on the starter motor brushes to the commutator.(Because they are burned/full of crap).

I forgot a few things: http://www.cygnusx1.net/Supra/Library/TSRM/MK2/manual.aspx?Section=ST&P=2

Download this entire TSRM. We all need this. This one is even indexed.

 

Dave nailed it! As stated above, the first time this happened, I too hammered a copper fitting into shape and cleaned the plunger and trimmed the brushes. That lasted about 3 years. It sure beat the crap out of the cost of a new or rebuilt??? starter.
The second time I had to do this, I replaced both solenoid contacts, the plunger that gets pulled into those contacts and the brushes. I might have replaced the drive end bushing as well but I'm not sure. It's been a little over 20 years and it's still working fine. Total cost was under $20. It's probably a bit more now but anyone that can remove the starter can certainly repair it themselves and save lots of $!
Truthfully, only one contact wears and the brushes weren't that worn but as much of a PITA as it is to remove the starter, it didn't make sense not to replace all the wear items. At least I knew what the problem was and that gave me plenty of time to source the actual Denso parts online cheap. It sure beat the crap out of the cost of a new or rebuilt??? starter... again and still. In the meantime, I kept a long rod and a medium hammer in the car. A moderate smack would always do the trick. It actually jars the plunger slightly. When you see these parts, you'll understand why it works.

 

Thanks for all the replies. It definitely was the solenoid in the starter. Took it off and sent it to a professional and sorted it out in no time. A very happy Supra owner again !

 

One of the few times when hitting it is genuinely the correct way to solve a problem!

My uncle's LS400 had much the same issue, he carried a block of wood to slip past the block to whack the starter with when it wouldn't turn, so I can vouch for this method too.

To clarify for any future people - getting the starter off isn't so bad if you're able to get comfortably under the car. It's held on with 3 bolts and will come away nicely (at least, it did when I had to take my gearbox off).