My advice would be to read through the basic care section of the main site
www.redearslider.com
There is wealth of information there on proper care of RES. It can be overwhelming at first, so ask questions as needed.
Room temp water is not satisfactory. My guess is that it is too cool for them. Not only will they not eat, they could be more prone to illnesses such as respritory infections and pneumonia.
Basic requirements are 10 gallons of water per inch of shell length, water at 78F for hatchlings, UVB and UVA lighting, water heater recommended. and a decent filter.
It will also help to read through the stickys in the different forum sections.
edit: to add to ferds comment, the pebbles can become impacted, and that can cause a loss of appetite too, but my first guess at this point is the water temp.