Can my computer, Hp Vectra VL400, run Windows 7?

Yep, just what I thought....
In the Drivers page, there are drivers all way down to Windows 3.0 up to Windows XP.
So, updating my specs!

768 MB RAM. Thanks Maxie and others! Edit 2 coming soon after install!

So, Edit 2:

Booting from DVD works. Windows Vista startup screen. Installation must be 65536 colors. After selecting Install Now, it says Setup is starting, and then dialog box. That's strange. It is blank. I just press where it needs to be "ok" 2 times, and then it throws me back away to Install Now screen. Any fixes?

Where did you get the Win7 installer? Try another from Clean Reinstall - Factory OEM Windows 7 burned with the tool provided.

You should have only your network driver in your backup so that if it's not provided during install you can install it to get online, enable Device Installation Settings, Check for Updates, then Install all Important and Optional Windows Upates until no more are offered after each requested reboot.

Then let us know which Display driver is installed. It may be adjustable to a higher resolution.

The Windows 7 Home Premium 32-bit DVD is legal, original. This happens when i'm installing Windows.

Work through the steps for Overcoming Windows 7 Installation Failures - Windows 7 Help Forums

Nothing can help there. I tried Diskpart, nothing. The same error box with no letters.

Did you try new installation media for your licensed version?
http://msft.digitalrivercontent.net/win/X17-58996.iso
Windows 7 USB/DVD Download Tool

So, I left Windows 7 ahead and I'm now installing Windows Vista Home Premium 32-bit. It's now at Expanding files 64%.

Yes, it installed succesfully. The boot time is around 20-30 seconds.