I think there is a clog in the nozzle, some filament is still stuck inside the nozzle/bowden tube, due to breaking when trying to remove it all.
Depending on your printer I'd say the best way is to heat up the printer to 260 degrees C or so, and either try pushing the filament out again, or take the hot end apart and the removing the clog(probably the melted plastic went up to far and cooled down in a higher part of the printer.
What do you mean by "skipped out of the nozzle in two pieces"? Pictures might help because I don't quite understand what you're trying to describe.
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