I have a toro lx500 riding mower. the blades won't engage.

Try rolling when you engage instead of in the still position may be too much on the motor, either that the belt is loose or needs to be replace. Or u need a carb adjustment at the idle.

In the northern US, I would use a 5W - 30 year round, or 30 in the summertime. Do not use "non-detergent".
In the southern US, I would use a 10W - 30 or 30 in the summertime. No non-detergent.

for any ride on machine that the blades don't engage id start at looking at occupancy seat switch , these are most times the culprits then if that's ok I move on to the actual engage switch and then on to clutch as last element

don't forget that past 2013 mfg machines operator must be in seat and weight over 80 lbs , the clutch pedal must be depressed and transmission not in reverse to engage the blades on a consumer grade lawn tractor (thank the CSB for that )

Havee you re-engage the tranaxles.; Otherwords taken out the bypass mode?

Check your seat switch first.

You are listed in the wrong section of Fixya. This section is for Cars and Trucks. List in a section more closely matching your product to reach an appropriate Expert.

.... burning rubber smell? Sound like you have done a cutter belt.

see if you have power and ground to the connector that goes to the clutch it could be a bad safety switch

if it has a electric clutch check for power to the clutch if no check the safety switches

You may have a bad starter - the solinoid is "clicking" but not engaging. Remove the starter and clean it up and connect it to 12 volts to check if can turn. If not then buy a new starter and replace it out.