You have to change your code like, 
print "file1 ="; 
$file1=<stdin>;
print "file2 =" ;
$file2=<stdin>;
@ARGV = ("$file1", "$file2") ;
chomp($remove = <stdin>);
chomp($replace = <stdin>);
while(defined($line=<>)){
 $line =~ s/$remove/$replace/g;
 print "$line"; }

[download]
When your code seems not giving the expected result, you can use the perl debugger to find out issue.
I debugged the code, after made the change from {} to ()
main::(./dynamic_file.pl:22):   print "file1 =";
  DB<1> n
main::(./dynamic_file.pl:23):   $file1=<stdin>;
  DB<1> n
file1 =file1
main::(./dynamic_file.pl:24):   print "file2 =" ;
  DB<1> n
main::(./dynamic_file.pl:25):   $file2=<stdin>;
  DB<1> n
file2 =file2
main::(./dynamic_file.pl:26):   @ARGV = ("$file1", "$file2") ;
  DB<1> n
main::(./dynamic_file.pl:27):   chomp($remove = <stdin>);
  DB<1> p @ARGV
file1
file2

[download]

In reply to Re: providing filenames dynamically by balakrishnan
in thread providing filenames dynamically by manish.rathi

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.