Hello I am using my second computer to gather some data and insert it into the SQL database. I set up everything when it comes to reading and writing the database remotely, and I can insert new rows just by using the normal SQL.
With pyodbc I can read tables, but when I insert new data, nothing happens. No error message, but also no new rows in the table. 
I wonder if anyone has faced this issue before and knows what the solution is.
The cursor.execute() method only prepares the SQL statement. Then, since this is an INSERT statement, you must use the cursor.commit() method for the records to actually populate your table. Likewise for a DELETE statement, you need to commit, as well.
Without more perspective here, I can only assume that you are not committing the insert.
Notice, similarly, that when you run cursor.execute("""select * from yourTable"""), you need to run cursor.fetchall() or another fetch statement to actually retrieve and view your query.
Inserting into SQL with pyodbc from remote computer