I agree with Ellencee. Check to see if the school has any insurance to protect you or your property while on campus during scheduled school.
And since you very probably have additional questions about your status, I offer the following:
1) "This morning, i was walking through the mud to get to one of my classes on time, when i slipped and fell."
Can you prove that you paying strict attention to your 'travel' at the time?? Can you prove that you took EVERY precaution to prevent your slipping?? Etc. These are just some of the questions that they would ask during any litigation that you might consider.
2) "This broke my guitar which I was carrying at the time. I was required to bring it for a school jazz band class i am currently enrolled in, and it was thus mandatory that i bring it every day."
Had you discussed any and all OPTIONS (storage, school supplied instrument, etc.) prior to deciding to bring your own instrument?? Especially one worth $1000.00.
3) "The unusual circumstances are that my school is currently undergoing construction. The only path to get to my class is either through the mud, or one of the two original paths left after one was closed for construction. If everyone had taken that one narrow walkway, it would have been impossible to arrive to class on time."
Did you discuss your concerns about the mud and your instrument damage PRIOR to the accident and ask if you could be allowed a few extra minutes between classes so that you cold take the more crowded route?
4) "I was wondering, if the school is somewhat liable?"
Depends on the answers to the above. And an issue of 'contributory' liability could come into play. On the surface, the best you could hope for would be that they were maybe 10% liable (if that), meaning that they would only be responsible for $100 of the total $1,000.
5) "In order to reach my class on time, i HAVE to walk through this slippery mud."
And what precautions (packaging, care, attention, etc.) did you apply for this mud?
6) "People fall on it all the time, it's just that I happened to break a $1000+ guitar."
Whoops!! There goes your whole case. You just admitted to having KNOWN that this was a hazard. Since you knew about it beforehand, and took that more hazardous route anyway, you just lost your case!
7) "Aren't schools required to label slippery surfaces?"
Generally, yes. And if they don't then they could be held fully or partly liable. However, as noted in #6 above, you already knew of the hazard.
8) "I thought this is somewhat similar to the law where if someone trips on the sidewalk in front of your house due to your improper maintenance of it, then you are liable for any damages."
Generally, you are correct. However, in this case, you were already aware of the hazard (which is what the sign would have done), so in essence, you chose your own path with knowledge of the hazards.
9) "The school could have put another path through the mud with wooden boards like they do when pouring cement, or simply extended the time we have to get to classes so that people would not be forced to go through the mud to get to class on time."
Yes, they could have done either of those. But that doesn't make them liable for YOUR choice.
10) "Is there any chance I could win this argument?"
Of course there is a chance. About the same as winning the lottery. But heck, someone has to win. Go ahead and consider filing a small claims action. It could be a good experience.
11) "Would the disctrict be willing to settle out of court for $1000, or even $500? It would be small potatoes to them, and their legal fees to defend against any lawsuit would be much, much higher."
This decision to settle probably wouldn't be made by the school district, but by their insurer (if the district even turns it in).
12) "After all, I could have broken a bone, or hurt myself badly if the impact was great enough to shatter a solid mahogany guitar neck."
What COULD have happened really has no relevance to what DID happen.
Bottom line....
1) Talk to the school. See if they are willing to help.
2) If that doesn't work, consider filing a small claims action (that is if your district isn't exempt from action).