using sysprep can make it work, windows will believe it is out of the box and install all of the drivers it needs. I did it from a Q9550 to a i5-3570k.
BUT you may need a new windows license as it will be an OEM license.
Also you are thinking, I imagine, of reusing the PSU, I wouldn't bother, the only thing your could reuse from PC#1 to PC#2 is the ODD, HDD and Case. The PSU will probably be rubbish and risk your PC#2 system.
If you want a non-gaming machine to tide you over, buy a laptop then you'll have 2 at the end of the whole process.
You are buying many things twice, just wait until you can buy them once, it'll be sooner or you'll get more for the same total amount of cash.