Timing should be the last thing to think about. The 3.3 / 3.8L engines use a timing chain, not a trouble-prone timing belt. Even if that chain did jump a few teeth, these are not "interference" engines. They won't run or won't run well, but they will crank just fine.
What do you hear when you said the starter engages? Is there a single, rather loud clunk from the starter? A single fairly faint click from the stater relay? A loud buzzing sound is also common for a defective or run-down battery.
You can start to get an idea of the battery's condition if you turn on the headlights, then watch what happens to their brightness when you try to crank the engine. Do they stay bright, get real dim, or go out?
The better test is to measure the battery's voltage. You'll need a digital voltmeter for that. You can find a perfectly fine meter at Harbor Freight Tools for $7.00. Also look at Walmart or any hardware store. Set the meter to the "20-volt DC" scale, then touch the probes on the two battery terminals. Which probe goes where isn't important. If you mix them up, you'll see a minus sign in front of the voltage. Just disregard that minus sign. We want to see 12.6 volts if the battery is good and fully-charged. If it's good but run down, it will measure closer to 12.2 volts. If you find it's around 11.0 volts or less, it has a shorted cell and must be replaced.
If the voltage is okay, keep measuring it while a helper tries to crank the engine. Tell me what you find for both cases.
https://www.2carpros.com/articles/how-to-use-a-voltmeter
Monday, April 24th, 2023 AT 4:40 PM