So you've got a couple things wrong with what you're doing.  The first is that you don't need a param component.  When the actionSupport fires, it will call the setter on your picklist and set the value so that it can be referenced by your other fields.

The other problem is that you can't rerender something that's not on your page.  You are probably referencing ids that don't exist.  For example, your "tickerInput" field will not be on your page if the picklist is not set to "Issuer", so once you actually do set your picklist to "Issuer", the actionSupport can't find the id of your component to rerender it, since it's not there.  So what you probably want to do is surround those last few inputFields with an outputPanel (which has no rendered attribute) with id="fieldPanel" or something similar, and then rerender "fieldPanel" instead of the three ids you've referenced.  Alternatively if this is inside of a pageBlock or something and you don't want to add an outputPanel, you can just rerender the parent pageBlock.  Does that make sense?

Finally, you may also be having a problem with validations.  actionSupport (and all other action components) do a form submit, so if there are required fields on your page or something, it may be trying to submit those fields whenever you change the value of your picklist, so the action may not ever really fire.  You can put the pageMessages component somewhere on your page to see if there are any validation errors.  The way to get around this is to surround your picklist field with an apex:actionRegion, which will tell the actionSupport to only submit what's in the region when it posts back to the server.

See these examples:

<apex:page standardController="Account">
  <apex:form>
    <apex:inputField value="{!account.industry}">
      <apex:actionSupport event="onchange" rerender="field1"/>
    </apex:inputField>
    <apex:outputText value="{!account.industry}" id="field1"/>
  </apex:form>
</apex:page>

 Notice that the above example works because the outputText is always rendered.

<apex:page standardController="Account">
  <apex:form>
    <apex:actionRegion>
      <apex:inputField value="{!account.industry}">
        <apex:actionSupport event="onchange" rerender="thePanel"/>
      </apex:inputField>
    </apex:actionRegion>
    <apex:outputPanel id="thePanel">
      <apex:inputField value="{!account.name}" rendered="{!account.industry=='Agriculture'}"/>
      <apex:inputField value="{!account.description}" rendered="{!account.industry=='Banking'}"/>
    </apex:outputPanel>
  </apex:form>
</apex:page>

 And note that this example rerenders the whole outputPanel because those fields won't exist on your page until you've selected either Agriculture or Banking from your account picklist.  Furthermore, it requires an actionRegion because account.name is a required field.  So if you remove the actionRegion and select Agriculture from your picklist, it will render the name field, and then if you try to select something else it will complain that name is a required field.  actionRegion prevents the name field from being submitted during the onchange of your picklist.