You may be a victim of Keyboard Ghosting:
"Ghosting" is the problem that some keyboard keys don't work when multiple keys are pressed simultaneously. The key presses that don't show up on the computer or seem to have disappeared are said to have been "ghosted".
PC gaming in general usually requires multiple keys to register at the same time - a problem that is not usually a factor when typing regularly (other than say, using the Shift-key). The problem can be prevalent in many game types, including racing games like All Stars Transformed - which require pressing a lot of keys in close proximity to one another.
Sonic All-Stars Racing: Transformed specifically uses a lot of slide-actions and activated powerups, as well as the steering controls, in order to control the game.
If this is the case, then you have some options for solving this:
1. Remap some of the more commonly-used keys
Ghosting only really occurs when keys are pressed in close proximity to one another. Use this tool to test different combinations of keys that you are likely to press, and remap some of them elsewhere.
2. Use a controller.
I would recommend instead playing All Stars Racing Transformed with a controller. The game was ported from the console versions (with many visual updates/upgrades and bug fixes to boot), and natively supports (and works well with) a controller.
As an example, you can pick up a wired Xbox 360 controller for use with your PC for about $15-$25 now, depending where you live. (The release of the Xbox One has slightly dropped their price). This is a solid controller with good native support on Windows, and is suitable for this purpose.
3. Get a keyboard with Anti-Ghosting
You can get keyboards with anti-ghosting capabilities. Some will only fix the common gaming keys (WASD and those in the vicinity), whereas others will fix most (if not all) of the keyboard.
However they can be expensive, and if you're happy with your current keyboard in other games and only have issues in All Stars Racing Transformed, I would instead stick to the controller.