To make sure no space flight, just make the planet a little heavier.
Based on chemical rockets, the cost to LEO is pretty terrible. If you increased the planet mass by a relatively small percentage, creating a chemical 3 stage rocket to deliver a payload (not payroll) becomes prohibitive or even just impossible. 25% more mass for the earth should do it.
Many other lift designs are possible, but we use chemical rockets for a very good reason, the other designs have even less thrust, or have other negative feature (a pulsed nuclear bomb a.k.a. Orion comes to mind).
Consider the retired space shuttle, its payload was 27,500 kg, but the launch mass 2,030,000 kg. I.e., the payload was not much over 1 percent of the total mass., were gravity only 2% higher, the shuttle would not be able to deliver any payload, etc. If you count the entire orbiting section, the mass is about 130,000 kg, which is still only about 6% of the launch mass.
Planes are a much different story, payloads can be a much bigger percentage because they don't have to carry their own oxidizer.
Some designs would be able to work with a heavier planet, but they will be quite expensive to develop. It is unlikely that such would ever happen without earlier experience with chemical rockets.
Recommended article, The Tyranny of the Rocket Equation
Michael Karnerfor does make a good case for balloon launch platforms in that you can at additional expense in development cost and per launch cost have a more efficient launch. NASA has explored this, figuring a possible benefit of about 25% fuel reduction (or conversion into payload). Similar arguments can be made for a number of alternative space launch ideas, such as launching from a plane, launching from the end of a sled on a ramp.
If you are persistent enough, you certainly could launch a small satellite from a balloon even with a 25% increase in planetary mass. You could find that you could only launch very small payloads (balloons are not a very stable platform), and they will be very expensive compared to our launch costs, esp. in higher development costs. Unless the value of being in orbit is well understood, no-one would bother. The lone exception in 1970 tech that I am aware of is using pulsed nuclear bombs, which have their own problems, such as releasing large amounts of radiation into the atmosphere and numerous EMP events.
Quite a few non-rocket solutions have been proposed, many are supplements to chemical rockets. The OP mentions 1970 tech level, most of the non-rocket solutions - including a balloon launch platform do not seem to be 1970 tech level.
Maybe you need a slightly more massive planet to keep the Michael Karnerfors out of orbit with 1970 tech, but the principle is simple, more planetary mass makes LEO much harder and it is already very hard. Maybe you think 25% increase won't stop all LEO at the 1970 tech level, OK how much then 35%, 50% - the principle is the same regardless.
Also note that micro satellites make less sense with 1970 tech under the heavy planet model. You need computers to do smart things to make a micro sat useful for many things. The Apollo guidance computer was introduced in 1966, it required 55 watts of power and weighted 32 kg. Because micro sats would not be useful for a large variety of tasks, the value of balloon and plane assisted launches would diminished as you could not launch large satellites without a very expensive launch platform. Vanguard is perhaps the best example example of what value of non-smart satellite could accomplish.
I believe several people are ignoring something. If the cost is too high compared to the value, no-one will launch things into orbit. For example, if you are willing to be ludicrous, you could launch a LEO satellite from sea level using chemical rockets on a planet with 200% of earth's mass. You would need perhaps 10 rocket stages to put a very small payload in LEO. The cost would be perhaps 1 billion USD per kg or more plus many billions in sunk development costs. It is not just a matter of physical impossibility, just that no-one would do it. The expected value would be far too small to motivate such an action.
So, maybe you think national pride, or a publicity stunt could motivate such a stunt. This seems very unlikely to me giving that the risk of a failure after spending a huge amount sum would still be quite large. Looks at the failure rate of the earlier orbital attempts -- and this stunt would be far more complex. National leaders, or publicity seekers do not like to be associated with huge failures either. I cannot envision anyone doing such a thing.
Just saw this new article on Real Clear Science -- they conclude 50% means we might be stuck here. Thet probably copied my stuff :-)