On your PC go to your Windows system drive > (normally hidden folder) ProgramData > Garmin > Logs > Express where you'll see at least one log file named "Express.log" and perhaps several more named Express_00.log; Express_01.log etc. in date order. If you can't see the ProgramData folder, check below (*).
Starting with the latest (it should be named Express.log) open the files in turn in a text reader and simply search for ".gcd". In the pic behind the spoiler below you can see i've found ".....PrimaryFirmware.006-B1697-00.5.60\software\nuvi55_56_560.gcd" which discloses the last fw loaded by GE to a nuvi 55 with HWID 1697.
Spoiler: click
You should find in one of your log files either
"....PrimaryFirmware.006-B0972-00.6.30\software\nuvinuvi13xxand14xxseries_GCDFile__630.gcd"
or
".....PrimaryFirmware.006-B1104-00.6.30\software\nuvi13xxand14xxseries_GCDFile-MTK__630.gcd"
That will definitively confirm the original HWID of your 1350 when it was made.
*If you don't see "ProgramData" folder listed in your Windows C:/ drive, you can make it visible and browsable by reading here: [Only registered and activated users can see links. ]. In later versions of Win OS, "Folder Options" is named "File Explorer Options" but the required settings are the same to uncover hidden folders/directories.
Once we're certain of its factory-set HWID we can know how to proceed safely, hopefully without causing more damage to it.
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