genes saved in sequence file look like this:
>hg18_refGene_NM_006511 range=chr1:15857951-15860804  
cctagtcacctgctaattaatctttttcctttcccctgtgttccatatagagaaaagtggtaaagaatct
+acctcactgggaATGTCATCATTACCAACTTCAGATGGGTTTAACCATCC
>hg18_refGene_NR_027268 range=chr1:28294033-28296656 
tttttttttttcttcttcttttttgtggagttgctttttttttttttcttcttttttgtgtcattgtttt
+tttaccatgtcctcagagtctggaattttacaaagtagttgctgagtaaacaggTAGATACAAATCAAG
+ATGAACTTTTCCGCAGGAGCTCTTATCATGAACAT

and the binding motifs:
>mot1
tttgtagatttt
>mot2
ggatcctttaag
>mot3
gtttaccccaa
[download]

Here are the actual sequnces I analyse: for GENES:

>uc002yje.1 chr21:13973492-13976330 
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaacccggccccgcagagccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
>uc002yje.1 chr21:13973492-13976330 
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaaaaaacccggccccgcagagccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
>uc002yje.1 chr21:13973492-13976330 
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaacccggccccgcagagggccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG

for motifs:
>ucmotif_1
gccccac
>ucmotif_2
gggggaaaaaacc
>ucmotif_3
agagggccc


here is the output:
 the distance is the following: 88
 the distance is the following: 20
 the distance is the following: 4
[download]

So, now the program searches for the first element in the first gene and for the second in the second and so on. I wish that it could find any of motifs for each gene if they present in it and count the length between the motif an exon start point (starts with capital letters).

I wish that it could find any of motifs for each gene

So it seems you want to test all motifs against every gene.  In case the list of all motifs fits into working memory, you could read them into an array (once, at the beginning), and then iterate over it for every gene.  Roughly sketched:

my @motifs;
while (my $motif = <MOTIF>) {
    ...
    push @motifs, $motif;
}

while (my $seq = <FILE>) {
    ...
        
    for my $motif (@motifs) {
        if ( $seq =~ /$motif/ ) {
            ...  
        }
        ...
    }
}
[download]