Sounds like you have excessive resistance built up in the cables - from either being loose or having excessive corrosion. The cable end could also have a crack in it, keeping it from being secured fully.
Loosen the bolt on the cables with a wrench and remove them from the battery (negative first, then positive). Inspect closely and make sure there is no damage. Clean the cables and battery terminals. Reinstall positive first, tighten down, then negative, tighten down. If they do not secure fully, you may need to replace the affected cable, or at the very least the cable end (not a great permanent repair, but ok for temporary use).
Try that first; you should also make sure the other end of the cables are secured entirely too.