Could we see the error you are getting? Any page can be the entry point, so it should work without problems.

I fixed one of the errors by editing "Page Properties" as well as renaming the file; the only problem I have now is when I browse to the root domain, a blank white page comes up instead of the default.aspx file. If I restore the original default.aspx file, the problem disappears.

So the name of the page is still "Default.aspx", you did not change it? In case you did, you would have to update the IIS configuration - Default documents section. In any other case, it may be an error that should be logged in the MonoX log file (see MonoX/ApplicationData/Logs folder).

Yes - renamed Login.aspx to Default.aspx (also tried lowercase). I don't know if this helps in any way, but when I copy default.aspx from a fresh install over to the wwwroot of this particular site, when I browse to the bare domain it shows the default page witht he blog module added, whereas if I just click on the "Home" button in the navbar it shows the regular default.aspx page as it should.

In looking at the logs, I see the following message come up frequently:

2010-11-17 16:17:27,652 [10] ERROR MonoX [220.165.14.182] - Error
System.InvalidOperationException: Personalization is not enabled and/or modifiable. The Enabled property must be set to true, and a registered personalization provider must be selected. The current user must be granted the right to modify personalization state.
at System.Web.UI.WebControls.WebParts.WebPartPersonalization.EnsureEnabled(Boolean ensureModifiable)
at System.Web.UI.WebControls.WebParts.WebPartManager.CloseOrDeleteWebPart(WebPart webPart, Boolean delete)
at System.Web.UI.WebControls.WebParts.WebPartManager.CloseOrphanedParts()
at System.Web.UI.WebControls.WebParts.WebPartManager.OnPageLoadComplete(Object sender, EventArgs e)
at System.EventHandler.Invoke(Object sender, EventArgs e)
at System.Web.UI.Page.OnLoadComplete(EventArgs e)
at System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint)

could this be related?

The error you found in the log file has nothing to do with the current issue: if you did not change the personalization settings in web.config the most probable cause for this behavior would be the authentication cookie expiration. For example, you visit a page, wait for a long period (so the cookie could expire) and than try to perform a personalization task (putting the part on a page, changing the part property, or something similar). MonoX is telling you than you don't have rights to do it since you are not authenticated anymore. Let me know if this doesn't sounds right.

Going back to the initial issue, if you plan to remove Login.aspx you should be aware of some consequences - for example, it is set up as a default redirect page for forms authentication (search for login.aspx in the web.config).
The behavior you are describing (blog part appearing on one page and not on another) can be easily understood if you take a look at how personalization works. Every time you personalize a page via admin toolbar, it saves the current settings in the database, with the currently active URL as a lookup key. In your case, you did some changes (added a blog part) on the root domain ("/") and saved them to the personalization system. However, "Default.aspx" is considered as a different URL by the personalization system, as you may change the default page name at any time, so it renderes the default content (without the blog part). Our recommendation is to use "/" in the navigation menu (by adding an "external page" with the "/" as the URL in the page management) to avoid such situations and maximize SEO rating for your site.

I didn't change personalization settings, but am still having problems making web parts stick. If I go to catalog and add a web part from the module list, the minute I go to design mode the web parts disappear from the page and go into the "Page Catalog" section. What am I doing wrong here?

Let me know which part are you trying to add and on which page and we'll go step by step. I can even do it on some of our live demo sites.

Just trying to add a blog container to a page and point it to one of the blogs I created on the left side, and then add a "newest posts" and blog list to the right side.

If you could just show me how to add a new blog container to a page and point it to a specific blog that would be plenty. When I try to add a new blog container to a page, if I click "Properties" nothing happens; from there, if I attempt to go to Design view the part disappears and only shows up again in the parts catalog under the "page catalog" section. If I could figure out what the problem is there that would help a lot. Maybe another web.config error?

I'm working on the site while it's online (since I'm using shared hosting) - if you'd like I can PM you the site address and you can poke around at your leisure.