Translation:I want to go online and listen to music.
To add to all the excellent examples on 了 and 乐, the name for this 'phenomenon' is 多音多义字 (duo1 yin1 duo1 yi4 zi4), or 'words with many pronunciations and many meanings'. Some of these characters have 3 or 4 pronunciations, and each pronunciation may have 1 or more definitions, as it were.
Other examples are:
1. 好 - hao3 = good, e.g. 好孩子 (hao3 hai2 zi3); or hao4 = hobby, interest, e.g. 喜好、爱好.
长 - chang2 = long, e.g. 长尺、长江; or zhang3 = oldest, leader, e.g. 团长、长子.
处 - chu3 = discipline, punishment, e.g. 处置、处罚; or chu4 = place, e.g. 妙处、处所.
As you progress along the course you may find more characters with such a characteristic. Enjoy the process of discovery and learning!
Characters can also alter their pronunciation in different contexts. When pronounced lè, this character refers to happiness (快乐 kuàilè), amusement (乐 lè), and optimism (乐观 lèguān). When pronounced yuè, it usually means music (音乐 yīnyuè), but can also mean happiness in this pronunciation as well.
From this wesbite (recommend you to check it out): http://blog.tutorming.com/mandarin-chinese-learning-tips/chinese-characters-with-various-pronunciations
In English, when "listen" has an oblect, it requires either "to" or "for" before the object. "to listen to something" means to percieve the sounds of something. "to listen for something" means to pay attention in the expectation of hearing something. E.g. "I listen to the radio every morning". - "Listen for my signal and don't do anything until you heat it".
Although both can be translated loosely as "want". The first has the sense of "I desire to", "I hope to" its use would be with regards to things and events in which the doing and the results are not entirely fixed or certain. In the second there is less ambiguity and the sense is more "I need to", "I have to". The difference would be for example be like the difference between "I hope to go tomorrow" and "I need to go tomorrow".
Had they said it your way in the exercise's translation, i wouldn't have bothered and entered the discussion which i usually hate having to visit and scroll through all its comments, hoping I'd find something that would answer my questions..
I think yours is an accurate chinese pattern