I had similar problems. Try removing the inverted commas and replace with apostrophes, so instead of...

onmouseover="rollover1.src="image/route.png"';"
onmouseout="rollover1.src="image/route2.png"';">

you have...

onmouseover="rollover1.src='image/route.png';"
onmouseout="rollover1.src='image/route2.png';">

Also, try removing the inverted commas before name...

<img src="route_files/route2.png" "name="rollover1" alt="" style="border: none; height: 225px; width: 300px; " />

so it's just...

<img src="route_files/route2.png" name="rollover1" alt="" style="border: none; height: 225px; width: 300px; " />