If it doesn't matter if the non-digits are consecutive, it's simple:
string nonNumericValue = string.Concat(value.Where(c => !Char.IsDigit(c)));
Online Demo: http://ideone.com/croMht
If you use .NET 3.5. as mentioned in the comment there was no overload of String.Concat (or String.Join as in Dmytris answer) that takes an IEnumerable<string>, so you need to create an array:
string nonNumericValue = string.Concat(value.Where(c => !Char.IsDigit(c)).ToArray());
That takes all non-digits. If you instead want to take the middle part, so skip the digits, then take all until the the next digits:
string nonNumericValue = string.Concat(value.SkipWhile(Char.IsDigit)
.TakeWhile(c => !Char.IsDigit(c)));
ABC123DEF. Would you want to getABCDEFin that case?