the mechanism of fastreport web is :
1. returning html which contains anitmated progress picture and a syntax to call webservice via ajax/xhr script, to enable calling webservice, you need to attach :
(note: MVC Razor style) @WebReportGlobals.Scripts() @WebReportGlobals.Styles()
2. in web.config, you must set webhandler to enable webservice
in system.web section:
<httpHandlers>
<add path="FastReport.Export.axd" verb="*" type="FastReport.Web.Handlers.WebExport" />
</httpHandlers>
double check the IIS installation features from the control panel (Programs and Features -> Turn Windows Features on and off -> Internet Information Services -> World Wide Web Services -> Application Development Features).
Interesting.....are you using Web Farm and Web Garden architectures?
from documentation :
To use the FastReport report generator in a multi-server (Web Farm) or multi-processor (Web
Garden) architecture there are additional requirements for creating special storage for data
synchronization between WebReport objects.
I know where is the problem. When is set application pool on 'Classic' mode , FastReportHandler isn't set on IIS in mapping service( isn't read from web.config ).
It have to be 'Integrated' mode. But why isn't work on 'Classic' mode?
IIS uses http handlers from both <system.web><httpHandlers> and <system.webServer><handlers>.
The solution is add precondition: integratedMode, therefore, if you use 'classic mode', IIS will not use handler with precondition 'integratedMode'
  <system.webServer>
    <handlers>
      <add name="FastReportHandler" path="FastReport.Export.axd" verb="*" type="FastReport.Web.Handlers.WebExport" preCondition="integratedMode,runtimeVersionv4.0" />
    </handlers>
  </system.webServer>
You have right. It's work. I had to be added <validation validateIntegratedModeConfiguration="true" /> in 'classic mode' .
<system.webServer>
    <handlers>
      <add name="FastReportHandler" path="FastReport.Export.axd" verb="*" type="FastReport.Web.Handlers.WebExport" preCondition="integratedMode,runtimeVersionv4.0"/>
    </handlers>
    <validation validateIntegratedModeConfiguration="true" />
  </system.webServer>
Comments
1. returning html which contains anitmated progress picture and a syntax to call webservice via ajax/xhr script, to enable calling webservice, you need to attach :
(note: MVC Razor style)
@WebReportGlobals.Scripts()
@WebReportGlobals.Styles()
2. in web.config, you must set webhandler to enable webservice
in system.web section:
<httpHandlers>
<add path="FastReport.Export.axd" verb="*" type="FastReport.Web.Handlers.WebExport" />
</httpHandlers>
in system.webserver section:
<handlers>
<add name="FastReportHandler" path="FastReport.Export.axd" verb="*" type="FastReport.Web.Handlers.WebExport" />
</handlers>
and
application pool in IIS Manager, another reference : https://msdn.microsoft.com/en-us/library/aa560277.aspx
from documentation :
To use the FastReport report generator in a multi-server (Web Farm) or multi-processor (Web
Garden) architecture there are additional requirements for creating special storage for data
synchronization between WebReport objects.
It have to be 'Integrated' mode. But why isn't work on 'Classic' mode?
IIS uses http handlers from both <system.web><httpHandlers> and <system.webServer><handlers>.
The solution is add precondition: integratedMode, therefore, if you use 'classic mode', IIS will not use handler with precondition 'integratedMode'