Engine is hard starting

The car is a Corolla FX and is carbureted, if that makes any difference at all. It always will be able to turn all the dash lights and radio on, but almost every morning it will take a few minutes to get started. When trying to start it the engine will usually turn over several times repeatedly, and then I'll let it rest and turn the car completely off. It takes me about three or four rounds of this to finally get it started and keep it started. But usually, if I can get it started in the morning, I won't have much trouble with it for the rest of the day. Sometimes, especially if it has sat for a few days, when trying to start it in the morning, the engine won't turn over at all. However the lights still turn on and a jump start will get it going right away. I had the battery and starter tested and they were fine. The battery terminals are very clean. Thank you.

Its a 1986 toyota corolla Sr5 hatchback 4cyl carburated. When its cold its hard to start and I notice that on the ground where my exhuast is its black on the ground and all around my exhaust is black too. Theirs also a really bad smell when im driving, when im just driving normally not flooring it its smells fine but when I speed up or slam on the gas it smells, catalytic converter? Also my car is leaking coolant I just havent been able to pinpoint it, I know it cant be the head gasket because the previous owner replaced that, and it leaks a lot, like a little puddle. Just today I started my car to park in the garage so the car was on for mayb 5 mins I look under the car and its leaking coolant. Could it be the intake/exhaust gasket?
Any help would be appreiciated, thanks.

Thanks a bunch for the quick response im goin to clean off my exhaust and get a new cat and see if it still smells or leaves black stuff on my muffler
and for the carb im goin to buy a weber carb, pricey but good performance, as for the coolant leak I might just take it to a auto shop and ask them to pinpoint the source of the leak.

O one more question
test pipe or high flow catalyic converter?

Hey again one of my friends recommended I get my carb cleaned out by a mechanic or do it myself and I wouldnt have to replace it.

Hello,
My Corolla is having some truoble starting when the engine is warm. Two pumps of the gas pedal (carb. Car) and it fires right up. When it's cold. When it's warm though it cranks and cranks and cranks and will finally chug to life, with a little help from me and the gas pedal. The plug wires are new within the last couple years, I'm going to replace the cap and rotor and the air filter is in good shape. What else should I be looking for. Again, this is a carburator car, not fuel injected. Thanks.

Hey again, so I replaced the cat with a new one, the odor is faint now. Also I wiped off all the black gunk on my muffler and drove it around for a bit with the new cat, theirs still black stuff on my muffler so im guessin its the carb. So im going to replace this thurs when I get payed. And also my friend checked my car and he said for the coolant leak he told me just to replace my thermostat. My question how do I replace my thermostat?

So I am having problems turning on the car when it has been working for a while and is warmed up. In the morning when the car is cold and hasn't been started, it starts up fine with no problem. After it warms up in 10-15 minutes while I am driving it, when I stop at a stop light it shuts off and its really hard to start it up again. Is there any suggestions?

Carbureted

I will check it out and will let you know

Lately my engine has been having some trouble starting. Replaced the battery, alternator, starter, and the spark plugs but I have to turn the key multiple times for it to start.

When I first turn the key there's no sound, no clicking, nothing. Then, I wait a few minutes (and turn the key again, really quickly) and it starts just fine. A tow truck driver jump started my car (about two weeks ago) and it made a noise it's never made before, since then I've been having this problem. The car needed to be jumped because I left the lights on and it drained the battery.

Also, the car now runs hot sometimes but as far as I can tell the cooling system is fine. I flushed and replaced the coolant, replaced the radiator and both the hoses, the pump works (the coolant circulates when the engine's running), and the fan turns on when the car is warmed up.

How do I find out what's causing the problem without replacing everything under the hood?