To start with, note that your question is itself un-grammatical. The word What is misused. You can either ask, Is this sentence ungrammatical? or Why is this sentence ungrammatical?
Now to answer your question: yes, this sentence is grammatically incorrect, and for several reasons:
1. It's a run-on sentence. In run-sentences there are too many clauses for one sentence, and the clauses are usually not properly connected to each other. These are your clauses:
Maria went to school today,
(she) checked out a book from the library that would help her finish her current event
She was HAPPY
2. You can't join clause #1 and clause #2 with just a comma. You need to follow the comma with a conjunction like and, and repeat the subject of the sentence with the pronoun she. The following are both correct:
Maria went to school today, and she checked out a book from the library.
Maria went to school today to check out a book from the library.
3. Clause #3 is unconnected to clauses #1 and #2, and it begins with a capital S. The first word in every sentence must be capitalized, and no other words in the same sentence can be capitalized except names, which are always capitalized. I would cut the third clause and include the information that Maria was happy in the second clause.
4. The word event is misused. An event is not something that one starts or finishes. It is something that happens or takes place. I assume you meant something like homework assignment.
5. In formal writing never capitalize entire words (like "HAPPY"). The following sentence is grammatically correct:
Maria went to the school library today, and she was happy to find a book that would help her finish her homework assignment.
I hope this answer was helpful to you!