Hardness of approximation without the PCP theorem
An example is this paper:

Guruswami, V., &amp; Khanna, S. (2004). On the hardness of 4-coloring a 3-colorable graph. SIAM Journal on Discrete Mathematics, 18(1): 30-40. link

Using the PCP-Theorem, Khanna, Linial, and Safra (2000) proved that it is NP-hard to color a 
3-colorable graph using just 4 colors. Later, Guruswami &amp; Khanna (2004) gave, among other nice things, a PCP-free proof for the same result.