Yes you still can play original titles on your modded 360. Since it is modded however, you should watch out for 2 things:

1) Going online can be risky. Microsoft has been known to ban users with modded machines who log onto Xbox Live.

2) System updates. Microsoft (and Sony and Nintendo) releases periodic firmware updates for its console. These updates may not be compatible with your modded firmware resulting in a bricked (i.e. dead) 360. Make sure you check whether the firmware update is compatible with the modded firmware you have before upgrading. Note that upgrading is compulsory to play titles released with the new firmware in mind, so you can't really avoid updating your machine indefinitely.

As to playing original Xbox titles what you need to do is to go to Xbox.com and check the backwards compatibility page. You need to download some software, burn it onto a CD, and install it on your 360. The site provides you with all the necessary instructions. This will let you player Xbox titles.

Halo 1 and 2 are the only titles that don't require the additional software to be downloaded. Anyway all the details are at the site.