It could very possibly be a hardware, driver, or recently installed software problem, but there's also a possibility that your graphics options have been changed which is much easier to fix. Either you or someone else may have changed these setting unknowingly or windows may have adjusted these settings because either your computer is not capable of displaying certain visual effects without a significant loss of performance, you don't have the recommended amount of ram installed, your graphics card may not be compatible with certain features or you are using too much of the cpu with certain features enabled.
Also windows aero must be enabled so there's a possibility that it's not, you can check this by right clicking on the desktop choosing personalize>window color and appearance>open classic properties for more color options and then look to see if windows aero is selected, if not select it and click apply and ok. Windows sometimes will change this setting automatically if you are using a program that is not compatible with windows aero such as divx players it can also happen if you are using programs to change the appearance of windows such as stardocks windows blinds which is suppose to be vista compatible, but really isn't.
You can check to see if it is the graphics settings by doing the following:
You can either open control panel>system and maintenence>system (or in classic view control panel>system) or you can simply Click start and type "system" when the results appear click "system" when the window opens look in the left hand pane and click advanced system settings, under "performance" click settings you should be on the visual effects tab. Look to see if any of the checkboxes are unchecked and if so check them to enable that feature. Also if the option "let windows choose what is best for my computer" is selected you may want to change this to either "adjust for best appearance" if you would like to have all of the visual effects enabled or "adjust for best performance" which may disable some of the visual effects, but make your computer run better or "custom" where you decide what visual effects you want to enable or disable. If you make any adjustments click apply and ok to let the new settings take effect, then try to open the taskbar properties again and see if you are able to check "show thumbnails".
Note: you may also need to restart your computer before the new settings take effect, but I don't think you do.
If this didn't work then the problem is probably one of the other things mentioned, try checking in device manager for any conflicts, check for driver updates and if neither of those work I would suggest using the sfc command to check for system file errors before resorting to a system restore or restoring from a backup.
