Review the sentence:
Sneezing and coughing, Emily's germs sprayed the computer keyboard.
Sneezing and coughing, a participle phrase, comes right before germs, an illogical target. A person, not her germs, does the sneezing and coughing! (Emily's, a possessive noun, functions as an adjective describing germs.)
Before you continue, review the rules for misplaced and dangling modifiers.