First of all, the BBCode you should be using is [noparse]... Any bbcode in that tag will not be parsed/translated into what it's actually supposed to be.
test
test
See? No silly * symbols to make things ugly. Next, you must have typoed your replacement, it should be:
Replacement: <pre>{param}</pre>
Now then, this issue comes from the "cleaning" that vBulletin does on outputting your stored data. See, vBulletin stores the line breaks in your posts with a \n character. The character is then translated into <br \> upon output - and in the source code vBulletin will insert a newline character after the <br \> so that the actual viewable source code on the page is pretty.
Your pre tag catches that <br \> html that vBulletin outputs and correctly outputs a newline. Then it catches the newline after the <br \> and outputs another newline. Can you dig it?
Anyway, without implementing a plugin or a change in the .php file source code - there is no way to resolve this issue. Although, a few (http://www.vbulletin.com/forum/showthread.php?t=231990) people (https://vborg.vbsupport.ru/showthread.php?p=1721294) explain that they've been able to achieve more desirable results with a different replacement value...
<code style="white-space: pre">{param}</code>
or...
<div style="white-space:nowrap; width:300px; overflow:scroll;"><code>{param}</code></div>
According to them, this replacement value works properly in firefox, but not in internet explorer. I haven't tested it... But you're welcome to attempt it.