Zoltan,
I own those headphones. They are not the "weak link," they are efficient. And what that means is that they don't require a lot of watts or current to do their best (I'm listening to mine directly out of an iPod Touch right now, and while it's not as good as my Senn 580s through an amp, it is very good.).
The reason why you're not hearing a big difference is because there is not a big difference.
Plug a pair of Sennheiser 650s or AKG 701s directly into your computer and they won't be driven properly. They require more power, and most soundcards simply don't have enough headroom. Your Audio Technicas work fine with your computer as a source, so the only big difference you're likely to hear is the loss of noise you might experience by getting the analog function of your DAC outside of the noisy environment of your computer. Maybe...just maybe, your computer isn't all that noisy. Mine isn't. Is it too late to send that amp back? When you upgrade to or add on a pair of demanding, high-ohm, inefficient cans, that will be the time to buy an amp.
In the meantime, you've gotten a whole barrage of typical audiophile board advice. IE: if your experience doesn't fit with their belief system (it is faith-based) , the fault must be somewhere else in your signal chain (throw good money after bad), or in your ears. Or the best of all...burn in. Yeah, that's it, keep the thing you're getting no value from until you're past the return policy deadline and you've talked yourself into hearing something that's not really there. Last but not least - "you have to listen for awhile before these advantages reveal themselves." Nonsense. Every scientific study on the subject ever conducted says we differentiate subtleties in sound best in a quick A/B comparison, and the basic science about memory makes it pretty clear that it changes, enhances, trends further away from reality and closer to what we want to believe with time. If you don't hear it now, you won't hear it later. Though you may imagine that you do.
Send the DAC/Amp back. Enjoy the music.
Tim