Yea, check the front ADD actuator. I have had the same problem (4wd not engaging) to a lesser extent, and I'm pretty sure it's my front ADD. On the plus side, the front actuator is a lot easier to get to than the T-case actuator. On the minus, it is still a couple hundred dollars to replace with a new unit. But I have read that you can regrease your old one and it will work better. I also find that exercise helps the actuator stay in shape. I have been leaving my 4Runner in 4WD more since it is a full time 4WD (like the v8s that are in 4WD all the time). I have actually wondered I remove my ADD--who wants 2WD anyway? I don't notice a difference in mileage.

BTW neutral is only needed for 4WD low, not 4WD high. A 2003 4Runner should be able to shift into 4WD HI in gear up to ~65 mph. But as mine has gotten older, it's more picky about going into 4WD. I have found slow driving 5-10 mph is usually the best to get it engaged.