When you render, you should use all the cores and CPUs that your computer has available at 100%. This should not crash your computer, if this is happening, there is a hardware problem.
Your Monitor is not related at all to the rendering process unless of course, you are using GPU rendering, in that case, your image should freeze or slow down the refresh rate. But that's related to Video card performance and not the actual monitor.
In any ways maybe your computer is not up to the task, your power supply may be too small for your CPU and video card, or you are just running out of RAM.
What are the specs of your Old all in one machine compared to your new machine?
You could also change the CPU priority to your software. Fire up the task manager then go to Prosses and select 3D Max app, the do right click and choose Set Affinity, the un check one core of all the cores displayed, this will let you at least one single core to run windows. This should ease your Windows performance, but if you are running out of RAM that's an other story.
Please post your computer specs to give you better advise.
