Help - Can I do an external pen-test in this network?

Hi,
 
I have just completed my classes of Penetration Testing and have been asked to 
do a project.
I have an option to do either external or internal pen test.

I can do an internal pen-test in one organization I've got, however, I am not 
sure how I can do an external pen-test in this scenario. The following is the 
network. Please tell me if I can do an external pentest in this case and where 
can I start.
 
Internet -> router / modem provided by ISP (only static IP in organization)-> 
Switch -> about 100 systems in internal network (pvt IPs).
Webserver & mails are hosted on public server. 
 
Ping: success
Tried nmap: Host seems down. If it is really up, but blocking our ping probes, 
try -P0 (we are scanning a router here, so it won't work)

Is there anyway I can get into this organization by doing an external pen-test. 
This is a small company into s/w development and uses only messengers to 
communicate with the outside world / clients etc. No major servers inside 
organization and none with pub IP address.
 
If you need any more info, please lemme know.
 
Regards,
Tushar

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