I have a old laptop that i had iTunes on. i got another laptop today... can i install itunes and listen to all my songs on the new laptop?

Yes you can!
www.apple.com/itunes/download/
Download it here. Good luck. Have fun. :)

Depending on the laptop's specs, you should be able to play the music from iTunes. iTunes is a huge memory hog, though, and will bring any system with less than 3GB of RAM to a standstill ¨C or, at least, you won't be able to run any other processes. The situation's better if you plan on using Mac OS rather than Windows, as the Mac OS version of iTunes seems to use less memory.
Next iTunes can only play a few audio formats: mp3, aac, and other popular music player formats. If you're an audiophile (like me) and like to listen to FLACs, VLC is your best recourse.

Five years of experience with iTunes on Windows, two on Mac.

you can connect them to each other and "share" your music to your new computer.

Yeah, you can. Install iTunes onto your new laptop. Then, copy all the music from your old computer to your new computer. After that, you can just add the music to your library...

Owner of an iPod Touch