Take it back to the shop where you got it. Maybe they can reinstall Mavericks for you (and verify that you can use a Terminal session).
Or take it to an Apple Store (after making a Genius Bar appointment). They should be able to re-install Mavericks for you.
As for no DVD, Apple made that decision back in the Lion days (10.7 - July, 2011 - 3 and a half years ago).
Considering the extent of Internet broadband access these days, and that many of their products do not have DVD, it makes sense going forward. And the not having a DVD is not just Macs, the iPhones, the iPads, the iPod line, plus the ultra thin, light weight laptops. Plus fewer and fewer people were even using the DVD drives they have. I have not put a DVD or CD into one of my systems in ages. I even replaced one in my iMac with an SSD drive.
And I'll just throw in, that people complained about the original iMac not including a floppy drive. The reality is that it was no longer suitable for the size of typical files such as music, pictures, and video and Apple just happened to be the first to see that. Apple built a phone without a keyboard, and everyone said they were crazy and it would not sell without a keyboard. Now the vast majority of smart phones do not have a keyboard and Apple is the largest company in the world. Apple took the telephone modem out of their laptops and put in WiFi. Apple has just released a Mac with a single port (it does a lot with that single port, but it is still a change in what used to be included with a laptop).
The point is that Apple is not afraid to throw away old tech and move forward. Other companies spend a lot of time and effort supporting old technologies at a cost.
This trend will happen again and again. That is the reality of buying Apple products.