Using SQL Database on remote PC.

Currently I have a program and sql database both residing on the same PC and all is working fine.
My current connection string is PubConnString = "Data Source=mikespc\sqlexpress; Initial Catalog=db_PigginGifts; Integrated Security=True"

I now wish to use the same program but with the database on a different PC eventually connecting over the internet using a static IP Address. To test this I have tried connecting to my own PC rather than connecting remotely and used the following connection string but although I do not get any errors I do not access the data in my database either.

PubConnString = "Provider=sqloledb;Data Source=192.168.1.65,1433;Network Library=DBMSSOCN;mikespc\sqlexpress; Initial Catalog=db_PigginGifts; Integrated Security=True"

My first question is whether it is possible to connect to a database on your own PC this way and if so what am I doing wrong.

You said you got no errors so I'd assume its working but then you implied its not. Could you elaborate ?

The opening form of the program has a combobox where the user can select a name before entering their password. This screen opens up OK and does not display any errors but the drop down box for the combobox is empty. The drop down list is meant to have a list of names retreived from a table associated with the database I am now trying to connect to.

I'd suspect that the query isn't working as you expect. Experiment with smaller queries first like simple Select queries to see if it works.