Despite these downsides, Experian estimates that up to 20% of car loans are taken out by those with a credit score in your range. So if you have the desire, you can probably find a lender.
The only question you have to ask is if you want to pay that much in interest. You might be better served by repairing your credit in other ways rather than taking on more debt. With a 420 credit score, you have plenty of room for improvement if you pay down old debt and eliminate any delinquent accounts.