According to the help iGrid 3.0 should be able to display on Win 7 and upward, but it doesn't. Other controls have no problem displaying/entering Korean characters. Am I missing something here?

Try to reproduce the problem in the latest release, i.e. 7.0. If the problem persists in it, send us a sample that demonstrates the issue.
There isn't much to reproduce the problem. It's a straight forward entering the data into the grid, store in the Jet db, then retrieve it to display in the grid again. Can iGrid 3.0 really handle unicode? Again, I'm not having any issue with other controls except iGrid.
The iGrid cell editor was rewritten from scratch to fully support Unicode editing only in the v4.0 - see the corresponding What's New on this page: 
Actually, it doesn't display the unicode characters even when they are entered into the cell directly from the database either. Can I get an upgrade or am I supposed to purchase again?
If you purchased a new license for iGrid or renewed it more than a year ago, then you can renew your license to get the latest iGrid. All license renewal options can be found on this page: 
I don't even need to type directly into cells, just display the chars. Do you have a bug fix for that? I don't really want to pay for one feature for only one customer.
If we talk about displaying text in a cell but not editing it, have you checked the font and its charset you use in iGrid? Does all this support Korean characters?

And have you tried the same in iGrid 7.0?
I tried
iGClasses.Font.Charset = 129
iGClasses.Font = "BatangChe" ---> Korean font name
but it didn't make any difference.

It seems to work fine with V. 7. I replaced some texts in Test.mdb with Korean characters and your demo app displayed without a fuss.
I do not remember exactly what we changed in iGrid trying to make it fully Unicode-compatible, but most likely there were changes related to text output too.

According to our rules of support, bugs are fixed only in the latest version of the product. Moreover, you need to have an active license to download latest retail builds with requested bug fixes.

We always recommend that our customers upgrade to the latest version of iGrid as it fixes all bugs revealed by now and also brings performance improvements and other enhancements.