evening,
Your printer model is about 5-6 years old, it looks as it doesn't get much use by the page count of about 3450 pages total, you have 0 flow on the grey cartridge.
The pgbk (thick black) is not flowing at all well, when flushing it, you didn't damage the printhead? the white bit (where you clip the cartridge into, the printhead, if you made a hole in this material, it would damage the print head. When flushing, you use should a bung on the syringe that goes over the white part of the head, this give its a air tight seal when pushing the cleaning fluid through, also to stop damage to the head.