You can do exactly what you have 🙂
var string = "|0|0|0|0";
var newString = string.replace('|','');
alert(newString); // 0|0|0|0
You can see it working here, .replace() in javascript only replaces the first occurrence by default (without /g), so this works to your advantage 🙂
If you need to check if the first character is a pipe:
var string = "|0|0|0|0";
var newString = string.indexOf('|') == 0 ? string.substring(1) : string;
alert(newString); // 0|0|0|0​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
You can see the result here