Obrigado pelo link SushiHangover.
Isso resolveu o problema:
apt-get install libapache2-mod-mono
Além disso, o httpd.conf continha
#MonoAutoApplication enabled
RewriteMap lowercase int:tolower
<IfModule fcgid_module>
<FilesMatch ".(aspx|axd|asmx|ashx|asax|ascx|soap|rem|axd|cs|config|Config|dll)$>
SetHandler fcgid-script
FCGIWrapper /usr/bin/fastcgi-mono-server4 .aspx
FCGIWrapper /usr/bin/fastcgi-mono-server4 .asmx
FCGIWrapper /usr/bin/fastcgi-mono-server4 .ashx
FCGIWrapper /usr/bin/fastcgi-mono-server4 .asax
FCGIWrapper /usr/bin/fastcgi-mono-server4 .ascx
FCGIWrapper /usr/bin/fastcgi-mono-server4 .soap
FCGIWrapper /usr/bin/fastcgi-mono-server4 .rem
FCGIWrapper /usr/bin/fastcgi-mono-server4 .axd
FCGIWrapper /usr/bin/fastcgi-mono-server4 .cs
FCGIWrapper /usr/bin/fastcgi-mono-server4 .config
FCGIWrapper /usr/bin/fastcgi-mono-server4 .Config
FCGIWrapper /usr/bin/fastcgi-mono-server4 .dll
Options +ExecCGI
</FilesMatch>
FcgidInitialEnv MONO_FCGI_APPCONFIGDIR /etc/mono-fastcgi
FcgidMaxRequestLen 204800000
</IfModule>
Ele se queixou de não conseguir encontrar / usr / bin / fastcgi-mono-server4. Não tenho certeza porque foi configurado dessa forma, mas eu comentei toda a seção inferior e desmarcou o MonoAutoApplication e agora está funcionando.