The EPP port mode is the desired mode for older printers. Check the cable to make sure there isn't a bent pin in the connector causing problems or a "pushed pin' in the female part of the connection (a female pin that has been pushed out of it's socket and not making contact). Also, try a different cable and make sure it's a good grade bi-directional cable, HP's are sensitive to the cable being used and it needs to be less than 3 meters (3 ft). Also make sure the cable is a "full pin" cable with all the wires, not one that has "minimum" wires as some control signal may be missing.
The printer/cable may work well with the Sony but the Sony may have slightly more current/voltage drive on the Printer port than the Dell does and the cable could still be an issue.
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Dell Inspiron 15 - 5577 Laptop
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Here is a file that may help -