I think the problem is that you're trying to build the Tr all at once. Use the conditionals to determine your branching, and leave the stuff that's not conditional (e.g. $ref->{'loc'}) outside of the if blocks. Construct the Tr after you've figured out what it's made of.

The below code doesn't exactly reproduce the functionality of your code, but it's probably good enough (or can be adjusted).

my @tds = ();
if ($ref->{'pic'}) {
    push @tds, $q->a({href=>"$ref->{'pic'}"},$ref->{'name'});
} else {
    push @tds, "<LI>".$ref->{'name'};
}

push @tds, $ref->{'phone'};

if ($type eq 'f' || $type eq 'c') {
    push @tds, $ref->{'fax'};
} else {
    push @tds, $ref->{'cell'};
}

push @tds, $ref->{'loc'};

if ($type eq 'c') {
    push @tds, $ref->{'con'};
} else {
    push @tds, $q->a({href=>"mailto:$ref->{'email'}"},$ref->{'email'})
+;
}

print $q->Tr([$q->td({-bgcolor=>$cellcolor},\@tds)]);
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