LINQ is for querying collections, not converting values. It is wrong to say you want to use LINQ to convert X to Y.
That said, here's the building blocks you need:
// string in decimal form to int
Int32.Parse("12345");
// string in hexadecimal form to int
Int32.Parse("ABCDE", NumberStyles.HexNumber);
// int to string in decimal form
12345.ToString();
// int to string in hexadecimal form
12345.ToString("x");
Then to do something like converting between decimal form to hexadecimal form:
var inDecimal = "12345";
var asInt = Int32.Parse(inDecimal);
var asHex = asInt.ToString("x");
Your "ASCII to (hexa)decimal" conversions could be done with a little bit of LINQ using the above building blocks. Assuming you mean the (hexa)decimal representation of each character's ASCII code:
var str = "FOOBAR!";
var asAsciiInt = String.Join(" ", str.Select(c => (int)c));
var asAsciiHex = String.Join(" ", str.Select(c => ((int)c).ToString("x2")));
// asAsciiInt == "70 79 79 66 65 82 33"
// asAsciiHex == "46 4f 4f 42 41 52 21"
var asciiInt = "70 79 79 66 65 82 33";
var charStrs = asciiInt.Split();
var asStr = String.Concat(charStrs.Select(cs => (char)Int32.Parse(cs)));
// asStr == "FOOBAR!"
var asciiHex = "46 4f 4f 42 41 52 21";
var charStrs = asciiHex.Split();
var asStr = String.Concat(charStrs.Select(cs => (char)Int32.Parse(cs, NumberStyles.HexNumber)));
// asStr == "FOOBAR!"