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Press and hold the Power button for 10 seconds or more, until the device restarts.
If that doesn't help, try clearing the cache and the data for the Calendar application, then restart the device again, and see if that helps.
So the touch-screen never responds to touch... its digitizer isn't working, or the like.
Is your LG phone an Android phone, or some other type? I don't know its model number yet.
OK, this phone in other words?:
If so, Android is what it runs.
And here are some groups of keyboard shortcuts for navigating without touch-screen:
There are other shortcuts, that apply to things other than opening apps (the first group) and navigating GMail (the second group)... there's also web browsing navigation shortcuts, and typing shortcuts shown here:
If you need the browsing shortcuts or another category let me know. If this answers your question in full, please rate my answer so that this case may be closed, and thanks.
That's possible. Try a standard USB mouse, nothing fancy, see if it works.
If you can possibly attach a photo of the keyboard, I will try to identify the MENU, SEARCH, ALT buttons for you. (Alt buttons are usually at the base of a keyboard, to either side.)
Unfortunately it seems that your keyboard doesn't have all the possible keys like the Alt, that make those shortcuts possible.
The Z and X keys look like they have promising 'Alt' functions - they must be activated somehow - but how? I can't see how.
Can the Alt key possibly be activated on-screen, maybe? if so, that may (unless that can be reached with e.g. arrow keys) be unusable under the circumstances.
You may just have to get the digitizer replaced on this phone, or better replace/upgrade to a new phone.