There are 2 main types of circular saws available. On either type, there is a gear case between the motor and the blade shaft.
One type is called a helical or worm gear drive saw. The motor shaft sits perpendicular to the saw shaft. The helical gears are the weakest point in these saws and the saw will act exactly as you describe when they are damaged. These saws are certainly worth repair but it can be more expensive to repair than an inexpensive saw.
The other type of saw is what we normally see, the motor shaft runs parallel to the saw's blade shaft. The gear case drops the blade shaft lower in the case so you can make a deeper cut. These saws can also act exactly as you described when there is gear damage. If this gear case gets damaged on an inexpensive saw, It's a good excuse to just replace it.
Check the owners manual and confirm that your washers are in the proper location as Handyguys suggested but be ready to budget a new saw if you can't make the old one work.