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You can appeal the denial, but it may be a difficult road. Unemployment compensation is for people laid off for a lack of work (through no fault of their own). It is not for people fire "for cause". Falling asleep at your job would be for cause.
I know its not an answer you are looking for, but please don't shoot the messenger.
The process to appeal this is outline here: http://www.uc.pa.gov/appeals/Pages/default.aspx
That should give you an overview of what you need to and can do moving forward.
I hope this helps.