I recently had to reinstall my Windows doing a complete wipe and now that I am back up I cannot seem to get Eador Genesis to run for some odd reason.

"The application failed to initialize properly (0xc0150002)" is the error I get each time I try to launch. I think I had this problem initially long ago and cannot remember how I finally got it working.

I am currently running Win XP SP3. SP3 is the version directly off the install disk as well.

My guess is, there's something missing with you fresh installation of Win XP SP3.
Get all updates for Win XP, restart your system and search again for updates. Do this until no new updates are shown.
Before searching for updates, you could also reinstall Service Pack 3. Maybe there's something wrong with the current installation.

Also install all components of DirectX9:
http://www.microsoft.com/en-us/download/details.aspx?id=8109
Run and extract the files to a separate folder. Open it and start DXSETUP.exe for installation.
Restart your system and run the DirectX Web-installer afterwards:
http://www.microsoft.com/en-us/download/details.aspx?id=35

You might also want to re-install the game after you got all updates.
And finally try starting the game with admin rights (right-click the game's shortcut, select Run as and choose the admin account).

This step shouldn't be necessary with XP.

Actually it seems that I needed to just run the window update thing like 5-7 times to finally get the update it needed. Think it had something todo with .Net Framework.

The problem was at the time my computer for some damn reason wouldn't recognize it's own built in Ethernet Port so I couldn't get online to update or find a Driver to fix the dang problem.

I ended having to scrounge a PCI Ethernet card from an old computer tower that no longer works and putting it in my main computer just to get online. Sad part is I still cannot find drivers to get the original, built-in Ethernet port working and since I don't even know what brand it is can't find a driver manually without going through a LOT of trouble.

I actually have quite a bit of exp in repairing and taking apart my electronics. It started back with my SNES. Between a friend and myself we had 3 non functional controllers. By taking them apart I was able to get 2 of them back in great working condition ;).