Q: I got a new computer recently and don't have my old laptop, which has all of the songs in my Itunes on it. I have all of the songs on my iPod touch, is there a way to transfer them to my new computer without having the old one?

If you do not have access to the iTunes Library on your Old computer... or its Backup...

See these 2 Links...

Syncing to a New Computer...

https://discussions.apple.com/docs/DOC-3141

Recovering your iTunes library from your iPod or iOS device

https://discussions.apple.com/docs/DOC-3991

If you do have access... See Here...

iTunes: How to move your music to a new computer

Or...

From your OLD computer...

Copy your ENTIRE iTunes FOLDER to an External Drive... and then from the External Drive to your New Computer..

Full Details Here  >  http://support.apple.com/kb/HT1751

An Added Bonus is that you will have a Backup of iTunes.

Recovering your iTunes library from your iPod or iOS device

What are the iTunes library files?

Use third-party software such as Phone to Mac - Pod to Mac or Phone to PC.

iTunes Store- Transferring purchases from iOS device or iPod to a computer

Downloading past purchases from the App Store, iBookstore, and iTunes Store