For reference, your car is probably worth about $400 in scrap metal alone. As in, if you drive it to the junkyard, they'll pay you $400 for it.
Running (needs significant work) is probably worth $1k, but that really depends.
The biggest limit will be your time and patience. Carvana and the like will cut you the smallest check, but they will do so today after a simple inspection.
The next highest will be private sales with a short timeframe. The longer you are willing to wait, the higher your final sale price will likely be. Also, don't be afraid to post it on multiple forums. Craigslist has dwindled in popularity, but it's still a very viable listing.
If you have a friendly personal mechanic, you may be able to enlist their help. Sometimes they maintain a project car for their downtimes, often from a customer that couldn't pay. They can tell you how much the car is really worth, or work out a discounted rate for slow repairs. Or they cut you in on the profits when they repair and sell it. But this only works with friendly personal mechanics, or shade tree mechanics.