You're probably having a problem using your device because of lack of internal space for running programs. You can use a very low level, low resource on the Android to remove programs. Install the Android SDK package and use it to uninstall some of your apps to regain internal memory. You can even use it to back up the apps on your computer so that after you have your android working again you can choose which ones to put back.
A good GUI program for managing your apps and deleting files from your android is Airdroid. However, you might not be able to install Airdrod until you've made space using the Android SDK package.
You can start out with these commands:
(You'll have to activate Debugging from the settings menu in the android to use this option)
This give a list of all the packages:
$ adb shell pm list packages
You can remove an app by running:
$ adb uninstall [apt-name]
You can use the "-k" option to retain your data/cache in case you will be reinstalling the app after you have gotten your android functioning.
You can us this command to see how much memory you have. This will allow you to know when you have retrieve sufficient memory to operate normally. It'll also allow you to identify better, if the memory is really your issue.
$ adb shell cat /proc/meminfo
You can look at Is it possible to backup apk from an installed application? for more tips on using the adb command.