Some malware changes the local group/security policy and prevents you from running a few things you described. I bet it also disabled the run function (Win+R). You will have to run a full system scan with a good AV (a list of some trusted vendors is e.g. here) to detect and delete the malware that caused it. Symptoms you describe are what I've observed before coming as unwelcome visitors (adware, not too pesky viruses) with some desktop beautifiers (themes, screensavers, icon packs,...).
@Luke has already answered how to scan your computer for installed malware. One thing to add is that if you can't restart your PC with a power on/off button, you could force reboot it with either holding the power button for 5 seconds, or pressing the reboot button, if you have it. If it isn't a laptop, you could also simply remove the power cord and plug it back in in few seconds. If it's a laptop, then some have a force reboot button on the bottom side that requires some thin stick to press it - a toothpick should do it. If you reboot your computer like this, make sure you're not running any disk intensive tasks in the background, and do a full file system check on next startup (it should ask you to do it when the OS detects an improper shutdown).
Anyway, you might still be still stuck with these things you described disabled even after the malware is gone. What you could do is check that there's no entries in your Windows registry under the key HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer (it would usually only have a single default value with no data set).
Navigate in your Explorer (Win+E) to c:\windows\ and open the regedit.exe file. Navigate to the said key and delete all the values in it and empty the data of the default value too, if it's been changed. To restore Task Manager, you will have to navigate in regedit.exe to the key HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies\System and delete all the ill-looking values there, too (possibly all of them, IIRC none should be there by default). That should restore all the functions you said you're missing at next reboot (and some of them actually immediately).
Make sure you run a complete system scan with your anti-virus again, after you've removed the local policy changing values in your registry. Of course, if your problems prove more persistent than you'd want them to be, then your best bet would be to nuke it from orbit and start from scratch.
