Installing or updating Windows 8 apps normally takes only a moment, but if your computer just can't do either any more then there are several potential causes. A corrupted Store cache is one of the more likely candidates, and fortunately Microsoft has provided a tool to help. Press Win+R, type 'wsreset' and press Enter. The Store cache will now be cleaned for you.
If Windows Update is broken or disabled then you'll also have app problems. Launch the Control Panel Troubleshooting applet (press Win+W, type 'trouble' then click 'Troubleshooting) and click 'Fix problems with Windows update' to detect and resolve any issues.