Try running these steps.
1. Go to umbraco.org and download there umbraco program to your local PC.
2. Unzip the folder and go to the web.config file and change the database connection to point to your SQL addon.
<appSettings>
<add key="umbracoDbDSN" value="Server=[DB Server Name]; Database=[Database Name]; User ID=[Database User Name]; Password=[Database Password]; Trusted_Connection=False" />
3. Upload the Umbraco site and its contents directly under your root directory.
4. Type in your address bar www.[mydomainname].com/install.
5. Follow the steps to fully install umbraco on our hosting server.
6. Once you have finished the setup process, you can configure the email to relay out from our web server.
a. Type in your address bar www.[mydomain].com/umbraco.
b. Type in the Admin login and password.
c. Click on the Content icon on the bottom left hand corner.
d. Click on the Home folder.
e. Click on the Contact folder.
f. Click on the Settings tab, and scroll down to ‘Mail Server’ and type localhost as the SMTP server.
This is the same steps I used to install umbraco on our server. I didn't try installing it on our subdirectory but I'm pretty sure you can upload it to a folder. Simply upload it to a folder and go into your hosting control panel and go to Web Application Tool. Set that folder as an application folder.