Mac Pro 5.1 Tower fails to boot up anymore

as others have suggested, and I quite agree, your Mac, its drives, it battery and it ability to start up and sleep are all working fine.

Your graphics card, the one with the display cable on it in slot 1, needs to be replaced. DO NOT replace with the same one that shipped in this Mac.

the cheapest is the Mac-Firmware GT120 card.

a reasonable alternative is the Mac-firmware AMD/ATI 5770 card.

If you are considering making the jump to 10.14 Mojave, you will need a Metal-capable graphics card, and that is a longer discussion.

I kept hoping that you would not have to replace your Apple AMD 5570, and that only the main port had died. so I kept suggesting using another cable and adapter, not knowing that you HAD another display (TV set) already connected via Mini DisplayPort to HDMI adapter. I was going to suggest obtaining a Mini Display to VGA adapter, but this whole line of reasoning is off the table because your card appears to be dead-dead.

if you remove the large VGA adapter from the main port on your 5770, you will see that its is the same connector as on the GT120 you're asking about. [Dual-link DVI digital, with Analog VGA in the bar and the four pins around it.] This is the same large connector on GT120 and many other cards.

So I think you already have all the adapters and cables you need, whichever direction you decide to go in.

Does the display work with another computer? Is it the computer or is it the display?

Do you have another video card?

Unless you can understand Apple Hardware test (and find something on which you can see it) then it may be a matter of replacing parts one by one until you find the one that is broken.

Many of these older Mac Pro silver towers shipped with worse cards than that one. The 5770 is a good card, and uses only one Aux power cord, is fairly quite and well behaved.

I had a 5770 where one port completely died, but the rest were perfectly good. I bought different display adapters and switched to a different port, and was able to keep using it.

Its cousin the 5870 requires two aux power cords and is Loud, especially at startup.

The GT120 does not need any Aux power cords. it can do ordinary work, but might struggle with editing videos or rendering wire-frame models. if you just need a card, the GT120 will let you do regular stuff without any fuss. And its cheap.

You won't find any of these cards sold as new.

on the 5770, be certain the card on offer is a Mac-firmware card, else you get no picture at startup, recovery, or similar times when full-blown MacOS has not yet loaded.

You did not respond to the other divergent questions:

What display are you using? Your current 5770 has THREE output ports, and you might be able to add an adapter to try a different port.

wait, WHAT?

Turn on the TV and fire up the Mac to see if the CARD is still working. If you need to toggle the sense of

[√]. Mirror displays ... type: Command-BrightnessDown.

if the CARD still works, only the Port has failed., and you don't need a replacement, unless you want Mojave.

¿What adapter do you use to the TV set? does it take Displayport directly? or does it use a converter to HDMI? or a converter to VGA?

moving the graphics card to a different slot is not a likely solution.

The left end of the card is retained by ... wait for it...

..the FAN, immediately to its left. There is a lighter-colored push button on the air-exit side of the fan.That button is barely visible in the full chassis picture you posted above.

Then the button is pressed, this allows the fan to slide to its left about 1.5 inches, and also releases the slim vertical shiny steel retainer-bar next to the PCIe connector. You typically need not remove the Aux cables to move up one slot.

that appears to be a VGA display. You can get an adapter, and move off the failure-prone larger port you are using now (digital DVI with Analog VGA) to one of the mini DisplayPort.

Here is an example adapter. (Don't pay to import this one from the US, comparable adapters should be available locally.) I cite this company because they know what they are selling and are not expensive.

Monoprice Mini DisplayPort 1.2a / Thunderbolt to VGA Active Adapter, White - Product # 12785 - $10.39

When your Mac starts up, by default it will turn on all connected displays that are plugged in and "ready to go". It will also light up a display when the Mac-end of the cable is connected, provided the display is powered up and ready to go.

If that TV gets a signal when your Mac is powered on, the graphics CARD is working, but the other port is not working.

The expected appearance for a powered on and ready TV and a working graphics card is the desktop background or the login screen pattern.

If you get nothing on the TV, then your card has likely died.

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that shortcut is for if you get picture, but it is just the background.

.

I see you have a white Mini DisplayPort cable plugged in to the adjacent Mini DisplayPort. What is that connected to?

Do you have any wish to move up to 10.14 Mojave? if you do, you should be shopping for a slightly different replacement graphics card, possibly one flashed for Metal and Mac Boot Screen support.

EDIT: NVIDIA cards are NOT supported in Mojave.

Do you have any desires to use hobbyist hacks to push your Mac Pro 5,1 even farther, beyond Mojave?

If so, you want to limit your choices to AMD cards, because NVIDIA support disappears after Mojave. In the US, these have been running around US$200 to $300 range on the used market.

If you're going to want to keep a G5 running in this day and age you are going to have to become a part-time computer repair technician. ;-)

You can open up computers of that vintage and actually replace individual components. Inside are many circuit board cards fitting into slots and one of these produces the video signal (I used to have 2 in mine). The nont-fun part about that these days is 15-30 years ago you just went and bought a replacement card for $20. Now you have to hunt for a vendor in old components. Apple certainly won't have them.

Now to me it is sounding like you may have a possible power source issue. Is the computer actually booting? If you are seeing that image you posted as a static thing it sounds like it is booting part way and then stopping. However, the image is also distorted so you may have multiple issues.

Realize that keeping a G5 going in this day and age is a labor of love. This one may need a lot of labor. I loved my G4 but about 7 years ago it developed a similar issue and I decided it wasn't worth spending the money and time on replacing a major component.

<< I don't know where the 5.1 in the header came from as I didn't write that. >>

Mac Pro from 2009, 2010, 0r 2012 that is running later than 10.11 El Captain has been revised to be a Mac Pro 5,1

You wrote that you had a G5, and I suggested the Hosts change the Title and remove your then redundant thread about 'should have been a Mac Pro, not a G5.' That way readers interested in Mac Pro 5,1 would read and contribute. Otherwise, that G5 in the title would make them skip reading entirely.