The Shuttle's problems started on march 20th 1979, just over 2 years before Columbia's maiden spaceflight.

When the stack took off from Edwards, hundreds of tiles were ripped off and that was the beginning of the Shuttle's problems. The tiles were its weakest link.
Because so many tiles needed to be glued by hands, because after every flight, they all had to be checked, because they prevented the shuttle from lifting off and landing under rain, the Shuttle never was going to be cost effective. But yes, the inertia was there and was still there after Challenger, so the program was maintained (payloads were built, international flights planned, the space telescope too...).

However, the money allowed for NASA also depends on psychological factors: in 1966, NASA went ahead of the Soviet Union, and the Moon was getting closer. In 1967, Apollo burned and Congress said: no more Saturn 5 than those already built and the budget kept going down.
If there had not been a shuttle program, there would have been much less interest in space and that lack of interest would have prevented an ambitious robotic program from taking off.
Same, after Challenger, the shock made it possible to pay for Endeavour.
But the shock after Columbia resulted in a very different path:away from LEO and back to the Moon. If everything goes well and routine takes over, so does the interest shrink and the money too.