You need to Contact CASE Singapore, there is a small charge but well worth paying. Of course it is illegal what they have done, and they would lose in the small claims court. These kind of things happen all the time here!
Though the problem is you are visiting, so they don't care! So VISA maybe your best alternative, though finding cheap isn't easy either
CASE will kick start negotiations with the Hotel, you shouldn't agree to anything, take them all the way to the small claims. CASE will not do that for you, they are just mediators. The hotel will get their backside kicked as Singapore wants to improve its tourism image, you may also wish to contact the tourism board and complain too!
https://app.stb.gov.sg/asp/index.asp
http://www.case.org.sg/
Property agents are even worse
