When i try to install a new software on my HP Compaq nc6400, Ubuntu freezes without sending any error code or something.
I thought it was only with Software Center that this problem happened but also happens using sudo apt-get in the Terminal

Please help, and thanks for reading

What is the name of this "new software" and where are you downloading it from? Difficult to assist you with troubleshooting if you don't tell us what you're trying to install.

I just found out the real problem: it freezes when i'm watching a video AND trying to install software.

I tried to install MyUnity but it wasn't on the Software Center, so i closed it and searched for a video about it. When i was watching the video I opened again Software Center (by mistake), but the laptop just freeezed.
After the reboot, I opened the video once again. While I was doing this I typed in the terminal sudo apt-get update and it freezed again.

I too have been havering lock up issues with my Acer AMD Athlon 64 with 4gb memory. Yes it happens during video and program installations. Like for sure this happens with the YouTube PPA and GMail PPA. Hope this gets resolved in some way.

I just searched askbuntu.com and you are not the only one having this problem.

One suggestion would be to use a more stable distro, and wait to upgrade to Ubuntu 14.04 once some of the bugs are ironed out (which probably won't actually happen, based on my past experience with Ubuntu ).

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I actually have a lot of experience with Ubuntu too. It really is a lot better if people wait until the July release of 14.04.1.

On the other hand I no longer install or recommend Ubuntu at all and the reason is pretty similar to your concluding statement. You just can't trust the OS.

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I have also have an AMD Athlon with 4Gbytes of memory. Also have an AMD RV710 graphic card (Radeon HD 4550). So the "good" news is that you are not alone. See my post here.

I decided to give 14.04 a try after taking out the AMD RV710 graphic card (Radeon HD 4550). Installation appeared to go well. However, as I customized the installation the computer became ever more sluggish. Eventually it froze. I experimented with several options to no avail. Finally, as a last ditch effort, I decided to do a fresh reinstall of 14.04, only to get the error message that the install "failed". At that point I gave-up.

I stuck my 13.10 disk in and reinstalled 13.10. Everything went smoothly. So I would recommend going back to 13.10 until the issue with the AMD Athlon is cleared-up.

Thank you everyone for your recommendations!

I think I'm going to install another distro instead of Ubuntu. I have in mind LXLE, Elementary OS or Manjaro..
I don't want to install Linux Mint or Fedora because my laptop is old and i just don't want to have a sluggish experience in them.

Can anyone recommend me another distro? I'm new to Linux... (Don't say Puppy OS because I dislike it)

I have heard that Ubuntu 13.10 was bad, it had many bugs

For me 13.10 has worked out very well. Regrettably, I am distro challanged so I can't really offer an alternative to Ubuntu.
You may wish to look into Mint, which is based on Ubuntu (good or bad? Depends on your viewpoint).
Mint, is supposed to be friendlier to old hardware than Ubuntu. Do a search on Mate vs. Cinnamon
A new version of Mint is scheduled to be released in May.

Do you think my old HP Compac will run it? I was thinking about installing it and also, in which Desktop Environment?

Sorry, I don't know enough. All that I can suggest is that you look up the minimum hardware specifications of Mint and compare them to your computer. Wikipedia link.

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Ok, i'll do that. Thanks!
But first i want to try out Elementary OS Luna, looks amazing and I heard it's lightweight so it may be perfect for me