Yep, after very very long time, I gave in and bought an Xbox 360. Gaming on PC is dead, long live gaming on console.

A: DisplayPort-to-HDMI adaptors and DisplayPort-to-DVI adapters are very simple and only operate one way.
For instance, when a DP-to-HDMI adaptor is connected to a PC that supports DP++ (multimode) capability, the
PC senses the presence of the adaptor and sends HDMI signals over the DisplayPort connector rather than
DisplayPort signals. No signal conversion is performed by the HDM adaptor. HDMI signals are merely passed
through. The unique DisplayPort adaptor capability enables the PC to connect to a variety of displays via
the DisplayPort connector including HDMI, DVI, and VGA. VGA adaptors are more complex and perform active
signal conversion from DisplayPort to VGA. These adaptors also operate only one way. Unfortunately, HDMI
does not support conversion to other display formats as does DisplayPort.

In other words, if you plan to connect DisplayPort → anything, it shouldn't be a problem. However, if you want to connect anything → DisplayPort, forget it. Or perhaps it is just HP ZR24w problem. Perhaps newer revision of DisplayPort handles it perfectly and I'm spreading FUD here. I honestly don't know. Go, and do your own research

After a bit of headache, I've bought pre-made HD/AV→VGA cable and it works. I was considering to DYI it myself, but cost of components went through the roof compared with a pre-made one. Of course, I didn't want to use cable shipped with Xbox. If you don't care about this, then it sure is cheaper to DYI cable by yourself.

I haven't noticed immediately, but only after a while of playing - the screen was off a bit. I've read on couple forums this is a “common” and it should be fixed(note: I have 16:9 display, yet I assume this is problem of 4:3 displays. Still, it can happen even at 16:9 displays). However, I couldn't find described “switches”(probably because Xbox dashboard got make over).

As of now, you go to the System settings → Console Settings → Display. There is menu item Reference Levels with options - Standard, Intermediate, Expanded. I've tried to play around a bit, but nothing has changed.

Then I went and played around with resolution. I mean from 1920×1080 → 1650×1080 and back and there we go. Screen got stretched correctly and stayed that ever since. Also make sure your display is correctly detected. This can be observed in Display section itself(prior to choosing resolution).

To recap:

1. Try to change resolution back and forth
2. Try to change Reference Levels combined with changing resolution
3. If none of mentioned above helps, cry for help

You should be able to get audio via HDMI. If you don't have HDMI(I don't), you have to get audio from composite cable. Beware though, because some videos on the internet show different Xbox HD/AV connectors which are no longer current(?). At least my Xbox shipped with a different one. I suspect video shows MadCatz Headset adapter, yet it states it is a standard Xbox cable.

Pitfalls:

• You can't use HD/AV together with HDMI, because there is “overhang” from HD/AV connector which effectively blocks HDMI
• HD/AV cable has two cinch MALE connectors opposite to two FEMALE cinch connectors shown in video

I've used two cinch(F) → cinch(F) connectors, one 2xcinch(M) → 1xjack 3.5mm (M) cable and connected to sound card via Line-in. Or you could use jack(F) → jack(F) connector and you will be able to connect headphones.

One noteworthy thing I've noticed. I'm not sure whether it is my sound-card or the cables, but channels, left and right, were switched despite the coloring of the cables. Instead red-to-red and white-to-white, I had, and have, to connect red-to-white and white-to-red. Otherwise you'll end up with switched L ↔ R audio channels.

I have to put this slight annoyance up. I have to. While redeeming your code, eg. pre-paid membership card, you have to enter billing address and telephone number. Telephone number. Really? Seriously? Never mind, I've seen this one elsewhere as well. Moving on. Ok, you enter billing address of yours only to find out: “Entered billing address or post-code do not match with console locale. Please, enter valid billing address.”. Right! Yes, it is very strange somebody has different locale from their billing address because of, I don't know, perhaps they've moved. Whatever the reason might be, I see no point in changing it only to please *you*, Microsoft. Chosen locale works for me and I'm not going to change it. I hope you didn't want me anything important, because there goes fake-ish address.