it's fine to say 'he would like to sell his car, but the man would not like to buy it' , right?
Can this be translated as "but no one will buy it"?
No. That would be "ingen vil købe den". In this case, the subject of the second clause is "manden" or "the man".
I wrote
"he want to ...but the man doesn't want to..."
Dulingo refused it. Why?
It could be because the first "want" should be "wants".