If I understand what you're trying to do in this code, I think the following should work, although I included the standard disclaimer that this is not tested, and I may have totally misunderstood your intent.

This code looks at each line of the input:

• The substitution pattern at [3] is probably not the best solution, but I gave it some light testing and it seems to work Ok.
• The lexical variable $line is omitted because it isn't used.
• [1] If the input line matches an SSI include of the type that we don't want, we do nothing with the line, which omits it from the output.
• [2] If the line is part of the body section, fix any anchors which refer to on-site .html files.
• Finally, we print to the output.

# always check the results of an open()
open (FILE, $filename) or die "unable to open $filename for input: $!"
+;

while (<FILE>) {

  # [1] omit line from output if it matches:
  # (make `[^.]*' more specific if only certain words should match)
  next if m~<!--\s*#include virtual\s*=\s*"/global_nav_[^".]*.ssi"\s*-
+->~;

  chomp;

  # [2]
  if (m!<body[^>]*>!i ... m!</body[^>]*>!i) { # modify body lines only
    # [3] replace .html with .asp in anchors in this line
    s~(href\s*=\s*")    # capture beginning of anchor in $1
      (?!http://)       # _not_ followed by http://
      ([^"]+)           # capture base of filename in $2
      \.html            # match .html
    ~${1}${2}.asp~gix;  # make substitution, global
  }

  print OUTFILE;

}
[download]

UPDATE: minor changes to substitution pattern. Thanks to japhy my regex hero.