Limp mode is usually a sign of excessive internal slippage, and generally means it is time for a rebuild.
Not starting in neutral could be a bad neutral safety switch. The switch should be on the drivers side of the tranny where the shift linkage attaches. You will need a 13mm socket and a 15 mm socket . You will also need a heat gun, the electrical plug is glued into the connectors and must be warmed up to be removed. These rarely go bad but they do get out of adjustment, or the shift cable bracket can get bent and get them out of adjustment. Loosen the two 13mm bolts and move it slightly in both directions and see if this fixes your problem before you change it out.
Beyond that, one of the gearheads who knows more about transmissions than I do will have to chime in.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)