My advice would be to move to .NET 4 hosting and use the .NET 4 package of mojoPortal with an Integrated App pool rather than Classic
If the problem continues after your host changes you to .NET 4 and you update the mojoPortal .NET 4 package and your host really doesn't allow any modules or handlers I would find a different hosting provider. If they can't give you .NET 4 hosting I would also move to a different hosting provider but I suspect they can do that.
Note that in changing to .NET 4 I would not combine that with an upgrade. You can find your current mojoPortal version under Administration > System Information then download the .NET 4 mojoPortal package for the same version. You can find older versions on the right side of our codeplex download page. Once everything is working well under .NET 4 then I would recommend upgrading to the latest version of mojoPortal.
Hope that helps,