How high can a ramjet go?
Here's a quick estimate for this.
The maximum altitude for level flight is when the engine can't produce the thrust required to fly fast enough to generate the lift required to balance the weight.
Ramjets work best at around Mach 3 and can operate up to Mach 6
Lift is proportional to speed squared and air density. So doubling the speed allows the plane to fly in air that is a quarter of the density.
The equations for calculating air density with altitude are moderately complex but there are a couple of tables here that show that the density at 32km is about eight times less than at 20km.
So if the SR-71 flew at Mach 3 and 25km, and if you could make a SR-71 that could fly at Mach 6, it might manage another 5 or 10 km in altitude.
Obviously that's a massive simplification because if switching engine technologies would have improved the SR-71's speed, they would have done it. Also because the SR-71 engines were ramjets when it was flying fast.
A ram jet won't get you into orbit because orbit is not just a matter of flying high enough but of reaching orbital speed - the speed where the curve of your naturally falling trajectory will miss the earth due to the earth's curvature. It's about Mach 25. And (as Ross points out) even if you could reach Mach 25, you can't circularise the orbit with an air breathing engine because that requires thrust at the highest point.