Not so long ago all screens were 800 pixels wide and they were square. There were two browsers (Internet Explorer and Netscape) and there were two main operating systems (Windows and MAC)
Today we have every possibel size screen (except the old 800 x 800); we have small, medium large; wide, narrow, landscape, portrait; multiple screen resolutions; at least five types of browser, some with as many as 10 different versions; we have phones, tablets, PCs, MACs, and newer operating systems such as IOS and Android.
Your website has to look good and be easily readable on all these systems and devices.
Computer screens (not to mention Internet TVs) are getting bigger wheras over half of all Internet seraches are carried out on the smallest smartphones.
You need an up to date site, properly coded - not just so your potential customers can view it - but because Google now actively downgrades websites with poor coding. So your old site stands even less chance of being seen.