I would start by following Will's recommended upgrade path.

http://www.willstrohl.com/DNNUpgradePath.aspx

I used it twice last week for DNN 2.1.2 to 5.1.1 upgrades, both upgraded fine

So... I tried the 3.2.2 to 4.3.7 install... following all the recommendations I could find... and the site won't load.

First - here's the procedure I followed to perform the upgrade - including restoring the site to it's original working v3.2.2 state.

1) Network Services needs Full Control to .NET Framework directories and C:\Windows\Temp directory. Set this before going further.
2) Try the upgrade again – try the install version of DNN v4.3.7 this time.
3) Stop IIS service (and dependencies)
4) Restore C:\Web to the working v3.2.2 version (from ZIP file)
5) Restore the MegabytePortal db to the working v3.2.2 version (from BAK file)
6) Reset ‘PortalUser’ permissions to MegabytePortal database by removing and re-adding login to db.
7) Start IIS & WWW services
8) Confirm that v3.2.2 site is working… YES IT’S WORKING FINE!

9) Run sp_removedbreplication @dbname = ‘MegabytePortal’
10) Delete all *.vb files in C:\Web\DNN3 directory & subfolders
11) Delete all DotNetNuke *.dll files (excepting module dll’s) in C:\Web\DNN3\bin folder
   from the purpleant.com blog – remove DotNetNuke.*.dll EXCEPT for DotNetNuke.module.*.dll files
12) Extract all files from the Install version 4.3.7 ZIP file into the C:\Web\DNN3 directory
13) Delete web.config, rename release.config to web.config & edit
14) Edit the 2 SQL connection strings & copy the 2 encryption keys - all else the same
15) Edit security on C:\Web - right click the ‘Web’ folder, go to Security, Advanced and click the
    “Replace permission entries on all child objects…” to force full access to all files.
16) Tweak SQL as follows to head off possible errors:
       - Rename MegabytePortal.dbo.EventLogConfig.IX_LogTypeKey_LogTypePortalID to MegabytePortal.dbo.EventLogConfig.LogTypeKey_LogTypePortalID 
          (this will compensate for the misnamed object in DNN install script)
       - The other script errors refer to creating objects that already exist so leave as is.
       -  Make the PortalUser account an ‘sa’ equivalent
17) Remember – the “PortalUser” account in SQL & the “Everyone” Windows group have ELEVATED permissions that will need to be removed after the install. (Everyone has full permissions to the C:\Web\DNN3 directory and subdirs)
18) Start IIS & dependencies
19) Confirm that ASP.NET for the Virtual Directory is set to 2.0
20) Confirm that App Pool is set to APP20
21) Run the portal website.
22) Install runs with 4 errors expected for objects that already exist.

So... that's the install...

Here's what I get when I run the portal website after the upgrade: