When printing the printed page comes out with a black streak down the middle of the back of document

check the drum or the heater roller in the fusing unit

Let me see if I got this right.

The received fax is clean but when you send one out it has a black streak on it.
Cool! So far so good.
Makes sense because for sending, the fax scans the original document and parts of the scanning area could be dirty and so on. Therefore a black streak may appear.
The same black streak would also appear when you make a copy, because the original document must also be scanned.
Logical!

However for receiving faxes, the machine uses the internal memory and the print engine only, and the same applies to printing the transaction report, which comes from inside via the print engine.
The scanner has no rol in either situation.

Now I'm lost!

.

This is becaue of incorrectly fitted toner or imaging unit would cause a black line at the the prints.
Also clean the printer drum.

Replace the cyan toner.

sounds like your cartridge is leaking. I'd try replacing the cartridge

Always try replacing the ink cartridges first.

It sounds like the print heads in the 7780 are bad. Don't confuse the ink cartridges with print heads. The cartridges fit inside the print heads. You will need to change the heads. Here is a link to HP's how-to.
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00841890&tmp_track_link=ot_faqs/top_issues/en_us/c00841890/loc:1&lc=en&dlc=en&cc=us&lang=en&product=2512010

Could have the same problem with the Dell.

Hello sir;The streak line from printing also should be from copy, because the line come from imaging unit, check the meter count if close to or over 50,000 then replace drum and drum blade, it will take care the problem.
The brother printer you need to replace imaging unit( drum unit).

Ok. You will likely need a new toner drum or cartrige. (usually you need the drum)

You should try changing the toner cartridges first. There may be something stuck in it causing the noise and streaking

if you need any parts for that machine a have 4of them

Thank You,

Mikey