The reverse button suddenly stopped working. Are there any trouble shooting tips?

The reverse buttons are usually due to grime. Go outside and shoot it with carburetor cleaner and constantly move it back it forth. You'll of course have to remove the top to do this. Once it is cleaned and unstuck use your sewing machine oil on all of the moving metal areas.

It would probably be best to begin the process of returning it to the vendor. Waiting may limit the ability to reach a good resolution.

If the machine has a buttonhole function, it may be set for that. This will cause it to sew in reverse

could you maybe while changing a bobbin or somehow , hit the Darning button its right next to the Bobbin release , a machine in darning mode wont advance the fabric and the traction feet go down to level with the platen (sign that it's in darning mode)

This button simply reverses the action of the feed dogs of the machine. Remove the thread plate and all the mechanism (bobbin, bobbin holder, etc) you can in the bobbin area. This should give you a better view of the operation of the feed dogs. Rotate the machine with the hand wheel to see how it operates. Continue rotating the hand wheel and push the reverse button. See if you can spot what's preventing the feed mechanism from reversing its rotation. Hopefully it's as simple as material or thread buildup in the mechanism.

Your reverse assembly needs oil. You should probably take it in to be serviced.

open the top of the sewing machine. Then press the button or lever that changes the forward reverse mode. You may find that something got stuck there where it should effect the machine part. May a drop of oil on that spot can help?

Cas: I'm going to give you a link to a google ebook that talks about these issues. Unfortunately, it's only a preview but it does show a great trouble shooting chart and mentions consew machines..

http://books.google.com/books?id=GLadvNufjaUC&pg=SA4-PA1&lpg=SA4-PA1&dq=sewing+machine+repair&source=bl&ots=RL9-FxFV_Z&sig=ZxOm_8lMAbm6uIActH_GwiFwXug&hl=en&sa=X&ei=d3ZLUIbyKcX9iwLh24DIDg&ved=0CFoQ6AEwBw#v=onepage&q=sewing%20machine%20repair&f=false

Good luck

You can download a free manual from the Singer Company website - http://www.singerco.com/accessories/manuals.html

here is a download for your manual

http://safemanuals.com/user-guide-instructions-owner-manual/SINGER/3116-_M

pg 32 talks about sewing in reverse sewing.
but doesn't give much on trouble shooting other than hold the lever while sewing. If that's not the case, then I think your feed dogs are the issue. check your feed dog drop. pg 9 part 12

If you think the reverse lever is sloppy, professional action should be taken, (take it in to be repaired under warranty?)

I hope this was helpful.