Please don't make things more complicated. I was talking about the Unofficial Patch for Oblivion (UOP), not for Shivering Isles and the DLCs. The UOP comes with 3 esp files which must be activated in Data Files. Apparently, Aurelio90 has problems extracting the UOP archive, not with anything Wrye Bash could fix.
Nor will Wrye Bash ever be required for installing or using the UOP, unless possibly when more mods than the UOP alone are installed.

I know that the Unofficial Patch for the DLCs may crash and that Wrye Bash is one way to avoid the crash (there are other ways, too), but this is about the UOP only.

There are two things that can really mess with an older game when installed.

1) Installing the game in the default windows folder. NEVER install in the windows folder. That will cause all kinds of issues with permissions and it can and will lock a game from loading, that will appear just like a crash on launch.

2) Turn off and keep off onedrive(proper setup is needed for it to not screw with your games). It is a cancer and will import setting for games from other computers that will cause your game to crash upon launch as the settings will not be appropriate for your current computer.

Here is another person's solution when Oblivion was crashing upon launch.

Had the exact same problem. Fixed it by turning off GOG's cloud-saves function and then deleting everything in c:\Users\User\Documents\My Games\Oblivion\ folder, including my old saves.

This would fit with crashing upon launch through Galaxy but not when you launch from the file in the system.

Sorry, only now I managed to open the computer.

About your question: I was trying to launch the game directly .exe, not from GOG Galaxy.

The TV I am using as current monitor is a Smart Monitor M5 27". Expect for Oblivion, I had no other problems with game installed in the new PC and visualized through the TV.

I made two different attempts to launch Oblivion from folder, both "vanilla" and then with UOP contents transfered into Oblivion data folder. Both the attempts failed.

Quite honestly, I don't know how to help you - as long as I don't have a clear picture of what's going on at your end.
For example, I still don't know what the resolution of your montor is. Not that I think it really matters (Oblivion does support very high resolutions "in general"), but just to have the information could help, as long as you don't know what the real issue is. If you don't know how to find out what the resolution of your monitor is, just say so.

Other examples:
- You also never confirmed that you did uninstall Oblivion COMPLETELY (including deleting the folders I oentioned, and, of course, the main Oblivion folder, too) before reinstalling it, and then launched it with default settings. If you did, what happened?
- You say you launched the game "directly .exe". Which exe? Oblivion.exe, Oblivion_Launcher.exe, both? What exactly happened?
- You say "UOP contents transfered into Oblivion data folder". But did you activate its esp's? At least the "Unofficial Oblivion Patch.esp" must be activated in Data Files.
- What about OneDrive? I asked several times, no reply yet.
[Edit: You did mention "old save data", but not in which context these may affect your current installation. Because of Galaxy cloud saving, or because of OneDrive or another cloud service? You also said "I'll have to delete this and see what happens". Did you do it (and how), and, if yes, what exactly happened? Although I doubt that old saves from your laptop alone could cause the Launcher to crash (while the game itself could possibly crash - it's why I distinguish Oblivion.exe and Oblivion_Launcher.exe).].
- And to clarify the Galaxy question took several attempts, too (after you had mentioned Galaxy in your first post).

I have no idea if any of the answers would help, but you have to start somewhere and then move on from there. There are so many potential problem causes, and the more you can exclude the fewer are left. But always bear in mind that the only information I have comes from your posts (and from what I know about Oblivion).
What I do know is that Oblivion "should" run on your PC (there is no general Oblivion-related problem preventing it from working on a PC like yours) - meaning that your system prevents it from running. But I don't know how, and If and how it can be fixed.

With that said: I'm not familiar at all with connecting PCs with TVs. Do you have another non-TV monitor (no matter which) you could connect with your PC? If yes, do it. Oblivion is likely to crash there, too, but to know is better than to assume.

IT WORKED!!! Just re-installed Oblivion for x time, then deleted "Oblivion.ini" and... I just launched it!

About @Greywolf1: thanks for your help. Unfortunately, English isn't my native language and I was unable to fully reply you stpe by step. Still, thanks again.

Great that it worked for you !
I wonder which setting from that file was responsible of the crash, but as long as just deleting it works it's all good.

Just one thing: isn't "Oblivion.ini" supposed to work along with mods?

No problem - it's more important that you managed to solve your problem.

But I have to note that you didn't follow my advice, which was to delete the My Games[Oblivion folder in Documents, nor did you tell me that you didn't. You could have solved your problem sooner by just following my advice.
And it would have saved my time, too.