Solution 1:

Windows 8 has several different views of the keyboard. Sounds like you just need to change to a different one. Here's the MS site for touch keyboards that I'll be explaining about.

In the bottom-right corner of the standard OSK (on-screen keyboard), there is an icon that looks like a keyboard for changing the style of keyboard. Notice the slightly different icon in the bottom-right corner of the second example OSK enter image description here.

(My apologies if MS decides to change the link locations.)

Solution 2:

Although this doesn't answer the question specifically, it addresses the issue the OP is unable to use some of the standard keys present in the physical keyboard but missing in the Windows 8 standard onscreen keyboard.

Answer is reported at http://answers.microsoft.com/en-us/surface/forum/surfpro-surfhardware/key-board-has-no-up-or-down-arrow/bf67308d-69c8-4afb-84bb-353ea2a88ba6:

"open pc settings in the settings charm select general scroll to touch keyboard enable "make the standard keyboard (...)"

When you invoke the onscreen keyboard options in the system bar, you will have a fourth layout available to you which presents all the keys found on the physical keyboard.