Hi,
I bricked both my 05EB boards and two CCDebuggers and had to get a third CCDebugger to help me recover from a similar situation.
It looks very much like your Eval Board hasn't got the right firmware programmed into it (any longer??)
Based on previous comments in response to your post, I assume you have tried to re-install the Eval Board Drivers and this hasn't solved your problem.
I suspect you haven't got the right bootloader/SmartRF04EB firmware in your Eval Board. When you do (and have Windows Drivers installed) Your SmartRF04 eval board will show up in the box (as in image you have supplied in your post), it will also appear in Windows Device Manager (under CEBAL CONTROLLED DEVICES) and in SmartRF Flash Programmer and SmartRFStudio (if you got these installed on your PC).
If you haven't got the right bootloader and firmware (perhaps have over written it - a common mistake due to convoluted design of tools), then to re-program your '04EV board you are going to need a CCDeugger or another 04EV board - to use as programmer.
I am currently working on a document for publication, that clarifies the ever so confusing official instructions and the relationship of various ports on the eval boards and how to check the right boxes in Flash Programmer to make sure that the right firmware goes to the right device and location.
Can you reply to this and let me know if this makes any sense and if let me know what (else) you have got by way of hardware (a CCDebugger? another EvalBoard?) and what firmware is programmed into them. Windows should certainly recognise these and they should show up in your Device Manager before you can begin to use them with the Development Tools and Environments.
Regards,
Tamer.