You have to be very careful with those packs as they don't usually have under-voltage protection for themselves. You're pack is likely fine but the charger isn't seeing the minimum voltage required to begin charging and so it won't.
I found myself in nearly the same situation not too long ago and managed to bring the battery back to a visible voltage by charging it with a Pb charge algorithm of similar voltage for a few minutes.
The multiple plugs are because there are multiple cells in the pack and each one requires individual charging (in parallel - not in series). They all have a common ground so you put the black end of the multimeter in the 4 pin black hole and put the red end in each of the 3 other colored wires. You will get 3 different, but probably close voltages.
I have this exact charger which is what I used to revive a similar pack: https://www.sparkfun.com/products/10473
Edit:
If you wanted to get a littler risky with the battery, a NiMH charger could be used for a short period as you mentioned. It charges at an acceptably low rate but the cells differ a lot more than they do between Pb and Li. A multi-cell NiMH for instance can have all of it's cells charged at once while this is generally not possible for Pb/Li. This means that a 12v NiMH charger is not going to work for a 12v Li battery since each Li cell needs to be charged individually.
If you happen to have an NiMH AA charger, you would retrofit that to be a 3v Li cell booster provided it slow-charges by putting two 1.5v terminals in series with the Li cell.
I would highly suggest getting an inexpensive smart charger as it's uses are nearly endless and it could save you many headaches that dumb chargers often create.
Additionally, you may want to build in a low-voltage cutoff circuit into your design to prevent this issue in the future.
