It seems like what you're trying to do is display "You picked hydrogen." if the user enters enter characters 'H' or 'h' or if they enter the string "Hydrogen". There's a couple of problems here..
Right now, the if(element[MAX] == ... part refers to the 61st element (0 is the 1st, 59 is the 60th) of the element string array. That's going to cause some problems right there. What you probably want to do is refer to the first character in the element array. So of the user types:
H
element will be equal to "H\0"
So you'd want to change the code to if(element[0] == .....)
The next problem is with the or statements. When you do if statements you test a series of boolean expressions. So let's say we have this code:
int a = 5;
if( a == 5 ) { do this... }
// the "a == 5" is the boolean expression here
else { do something else }
A boolean expression is false if the value is zero or NULL.
It's true if the value is anything besides zero or NULL.
So:
if( a ) { cout << "not zero\n"; }
else { cout << "is zero\n"; }
This means that the code (I changed it some here) has a problem:
if(element[0] == 'H' || 'h' || "Hydrogen"
The last two parts (|| 'h' || "Hydrogen"

will always evaluate to true (they are nonzero), so this expression will always be true (ie, x || 1 || 1 ). The code is actually not comparing the value of element[0] with the 'h' and "Hydrogen"..
What you really want to do is something like:
if( (element[0] == 'H') || (element[0] == 'h') ||
|| (element[0] == "Hydrogen"

)
//this last part needs some changes described below
The last problem has to do with the 'Hydrogen' part of the or statement. You refer to single characters with single quotation marks. You refer to strings with double quotation marks. That's why the words Hydrogen were changed to be surrounded with double-quotes. That's not all though.
The expression (element[0] == "Hydrogen"

doesn't make sense. The code is comparing a character to a character array. What you're trying to do is compare a string to a string. C has this function called strcmp (in the string library, so make sure to #include <string.h>) which compares two strings. You call it with int temp = strcmp( string1, string2 );.
It will return 0 if string 1 is equal to string2 (or, their lengths are the same and the characters inside are the same).. or a nonzero value otherwise.
So what you want is: (strcmp( element, "Hydrogen" ) == 0)
If you put it all together then,
-make sure to include <string.h> in your file
-change the if statement to:
if( ( element[0] == 'H' ) || ( element[0] == 'h' ) || ( strcmp( element, "Hydrogen" ) == 0 ) )
hope this helps..
indd