Things that you can't have: blood and guts, monsters/aliens, car chases, grizzly bears, ghosts...etc.
This leaves you with a lot of possibilities, but very little room for making something actually scary. If you want to go with the ideas above then you'll have to work very hard in order to produce something that both makes sense and is genuinely frightening.
My suggestion would be to use an unseen but identified threat. That is to say, some sort of malign force is at work but for the purposes of both tension/cost you keep it out of camera shot. Think Blair Witch Project. At no point do you actually see the psycho and/or any of the characters being harmed. Take The Last Exorcism- we 'suspect' that a demon is at work, but the evidence is purely derived from our own suspiscion (except for the crap last 5 minutes.)
So what could you use? Just to throw up a scenario:
A guy is walking his dog through a wood. Along the way there are lots of posters put up but he passes them by without noticing. Eventually he goes up and takes a look at one of the posters and it is a police warning that there is a lunatic escaped from a prison for the criminally insane and he has been spotted in the area. The man is then caught by a great desire to get home but along the way he begins to catch glimpses of things/hear sounds that make him convinced that the lunatic is in the forest with him. Eventually his paranoia drives him into a frenzy- then it would be up to you whether to end with the lunatic being real or a figment of his imagination.
I'm not saying this in order to give you a storyline, I'm just saying that you could easily shoot that sort of film in some deserted woods with a couple of mates, some printed WANTED posters. It doesn't require any special effects but can be very effective. I just worry about the practical difficulties of creating a storyline based on 'the fear of fear itself'.
Sorry for the overly detailed post
