Can you confirm you do indeed have the Android market installed on your tablet?
I notice you say other apk's work if already installed, which suggests to me you may have been trying to install market apps from a web browser on your tablet.
This could be causing your problem, I'll explain why and how to sort if if this is the case.
I did some research on the model tablet you said you are using and it is a generic brand from Shenzhen in China which is released by different companies under different names.
On most of these devices you need to install the market, and to enable non market sources as well, I found a page showing how you can do this at
How to Install Market APK app on Your Apad/Epad/Gpad/Chinese Android Tablet or Phone | China Phones Reviews
This may solve your problem.
Dave