while read line
do
   #Get Line Number 
   OLDLINE=`sed -n $Lineno $filename`
   echo "Un Changed Line : "$OLDLINE
   echo "Enter a New Pattern : "
   read NewPattern <&1
   echo "NewPattern :"$NewPattern 
   NEWLINE=`cat $filename | sed -n $Lineno | sed s/$OldPattern/$NewPattern/`
   echo $NEWLINE
   LINECHANGE=`sed s/$OLDLINE/$NEWLINE/ $filename`
   echo $LINECHANGE
   ChangedLine=`sed -n $Lineno $filename`
   echo "Changed Line : "$ChangedLine
done < $INT_FILE

LINECHANGE=`sed s/$OLDLINE/$NEWLINE/ $filename`

$ cat ea.txt
root 1933 1923 localhost calm 32rhewr

$ A=root

$ B=ROOT

$ sed 's/$A/$B/g' ea.txt
root 1933 1923 localhost calm 32rhewr

**No change above

So use double quotes instead of single quote: 

$ sed "s/$A/$B/g" ea.txt
ROOT 1933 1923 localhost calm 32rhewr

So 

LINECHANGE=`sed s/$OLDLINE/$NEWLINE/ $filename`

should be something like this:

LINECHANGE=`sed "s/$OLDLINE/$NEWLINE/" $filename`