No, badly applied paste has very different symptoms. If you put too much paste then you will be looking at a heat problem. This would not show up by not POSTing or stop your PC from turning on. It would also not stop your Windows installation failing. It would instead cause crashing, hanging and possibly erratic behavior (spontaneous rebooting etc). Modern CPUs clock themselves down drastically when they detect rising temperatures so they can feel sluggish.

You can check for sure by using any number of benchmarks or soak testing tools.