Used cars, and ones that are so old and have so much mileage on them that they sell for only $1100, are usually sold "as is," with no warranty and with the buyer being responsible for having their own mechanic inspect the car, reviewing all maintenance records and a CarFax, etc. etc., and assuming the risk that for $1,100, you had to have expected to put some money into this car sooner or later, and with a used car it can be in 2 hours.
If you can get the seller to replace the car, great, and/or if you can get them to agree to do in writing, then you have a written contract you can enforce. It will be hard, but not impossible, to enforce this oral contract to replace the car in Small Claims court. You can expect the seller to deny ever agreeing to this, and relying on the fact that it was an "as is" used car sale with no warranty.
Oral contracts are enforceable in CA, and are proved through witness testimony (your own, and anyone else who heard it with their own ears or saw it with their own eyes), written tests, emails, contracts, etc.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
I'm sorry to hear about the problem you are having with this car. Given the facts you are presenting, I would certainly recommend small claims court if the seller fails to give you your money back. In California, there is an implied warranty of merchantibility which protects buyers in cases like this, which says, basically, if someone sells you a car, it has to be at least usable as a car for a reasonable period. Certainly, this car would fail that test.