I have a pair of beats solo HD for about a year and a half now and the cable stopped working. I'm looking to replace the cable but i was wondering would a cheap headphone cable sound bad compared to the original beats headphone cable?

Some believe it does, some believe it doesn't.

All I can tell you is that in my own experience & opinion, any decent quality cable works fine.

In my personal experience, there is at least one headphone series that does make a difference with cables.  Most don't.  The glaring exception is the Sennheiser HD580/600/650 series of headphones.  A Cardas cable will remove the "veil."  One might even say the HD600 approaches Grado-like quality with a Cardas cable (probably an exaggeration, I'll admit).
 
There is a wide range of reactance and inductance besides just resistance in a cable's makeup.  Perhaps some headphones are more sensitive to it than others.  Personally, I think the prices paid are outrageous for some of this stuff.  A friend supplied me with the Cardas cable for free, so I have no investment to defend.  Yet, it made an easily audible difference in my HD580 and HD600.  The HD580 sounds positively dead without it, for instance.
 
Even so, I'm not about to go out and buy more custom cables for my other headphones - I'd rather make them myself if I was so inclined - but I'm not.  There are easier things to make that will make much more difference - amps and DACs, for instance.  That said, the one exception seems to be the Sennheisers.  I will admit that much.