Throw them away. They have been treated like trash, and are trash now because of that.

In addition to the visible damage there will be more invisible damage.

They are SMD components (surface mount). Usually the ones that start with "L" are inductors, and the ones that start with "C" are capacitors. As far as the sizes, you'd have to measure. You can print out a 1:1 size chart. As far as the values go, you'd have to measure, or just buy a dead board as a donor.

Here's a size chart with drawn-to-scale components.
https://cdn2.hubspot.net/hubfs/3932677/Sizing_Chart-D-1.pdf

It's hard to tell with SMD components. C* is always a capacitor but the value can be anything form pF to uF range. These are power filters so the smaller ones are probably 100nF and the bigger ones can be 1 or 10uF I guess. Look like 0603 and 0805 size, but possibly the zoom is tricking my eyes and it's 0402 and 0603.
The L* are small inductors, these are going to be very tricky to get right. But the small parts are usually just simple ripple filters and I suppose just bridging them with a piece of wire would work in a pinch. At least the card should boot if that was the problem, but might be unstable.

@ retardware
I don't agree. I don't think its right to give up, just because of minor damage. If all fail, at least the board can become a donor to another board.

@ wiretap
Thank you for the chart and info. And the correction SMD, I really appreciate the help !

@ Deunan
Thank you for elaborations on wiretap's comments. Which components could I try to bridge in a pinch? When trying to boot with the card, the fans spin up and LED light turns on, on the one fan, but not the other, but then they stop. Like the board is trying to boot, experiences an error and stalls. No picture at any point.
There is no visible damage from overheating, burns or corrosion.

Additional info on the cards:
The red card is a Gainward FX5900, the blue is Hercules 3D Prophet II TI. I think both cards are special enough, at least to me, to attempt to revive them.

Well, as these cards apparently are not low end (which I won't bother to repair), then my advice would be to just take conventional leaded ceramic caps 0.1uF and solder them into the red board, to see whether the card boots (if the card is okay otherwise, it might even work without these, though possibly unstably.)
If it works, then you know it makes sense to salvage some caps from a dead board.

Putting bridges is easy, just bend a component wire into "L" form, with the horizontal end having matching length so that it fits the pads. Then you can easily solder it in and snip off the excess part.

You can generally follow @wiretap's and @Deunan's advice, both are very competent.

Where are you located? I have a PACE PRC-2000 professional board rework station and some board repair experience, I could give it a shot if you paid for shipping and the parts. You really need a solder paste dispenser and a reflow wand to solder SMD parts accurately. Also, you can probably infer the value of those components by studying the values around them. I wouldn't bridge anything, especially since some of those are most likely capacitors and will not respond well to a bridged connection.

@ retardware
I am glad that you agree that some cards are worth spending some energy on. I agree that low-end budget cards not are worth the effort if you can easily or cheaply pick another one up.
Thank you the advice on both the caps needed for a test "job" and the maiden voyage, as well as how to bridge the gaps (I am just worried that I will fry something)

@
dkargut
Thank you for the offer, that is very generous! Unfortunately I live in Denmark and the round trip to US and back again would be around $50 estimated. Not saying I am not considering taking you up on the offer (:

Have you tested those cards? Missing decoupling capacitors are not critical for graphics card operation, its purpose is just to reduce noise in power supply of nearby active element.

In the first photo, you can notice that circuit is symmetrical and should be the caps, desolder C581 or C633 and measure it. Same goes for under GPU caps, there is a good chance that all of those bigger light brown MLCCs are of equal value.

GF2 card does have inductors installed, I wouldn't bother replacing them if soldering job looks good.

SSTV2 wrote:

Have you tested those cards? Missing decoupling capacitors are not critical for graphics card operation, its purpose is just to reduce noise in power supply of nearby active element.

In the first photo, you can notice that circuit is symmetrical and should be the caps, desolder C581 or C633 and measure it. Same goes for under GPU caps, there is a good chance that all of those bigger light brown MLCCs are of equal value.

GF2 card does have inductors installed, I wouldn't bother replacing them if soldering job looks good.

Hi SSTV2

Yes I have tested both, the Hercules fan spins, but no picture (the card is also missing additional two smd capacitators) and I researched some more and realize that the two inductors are from the factory, some versions look like mine and others different, but both "legit".

The mission SMD's

The Gainward FX5900 fans also spin, one of the fans blue led also light up, the other fans are not lit. The card then shots the fans down after 5 seconds. And the fans spin shortly when I hold the powerbutton to shut the machine down again (open air test bench on ASUS TUSL2-C with 1.4 Tualatin)

Those two caps connects to a wide trace, which is for power most likely, no big deal that they are missing, but if their absence unsettles you, just install caps between 10 and 100nf and that will be good to go.

Now, if you get absolutely no picture, it means that GPU does not work or get initialised, it could be caused by: corrupted bios, faulty GPU voltage regulator, cut traces, short under GPU, faulty GPU die. Graphics card with completely absent memory or its power, would still output garbage video and motherboard would not beep error code for missing graphics card.

Please also note that quartz crystal resonators are very sensitive to mechanical shock, more than anything else on that board. If the quartz wafer in that metal capsule has shattered, the GPU does not get any clock signal and will therefore seem to be dead, even when perfectly intact.