Greywolf1: If you receive an error message saying "corrupt", the the savegame is very likely really corrupt, and it could be a real Oblivion problem (not Galaxy, or cloud saving). I've never seen this happening myself, but I read that this does happen.
To convince yourself, please create a new game in a new Oblivion installation (no mod, no unofficial patch, no OBSE, ...), and save it as soon as possible. Then exit Oblivion, relaunch Oblivion, and load the savegame you just created.
If you get the error message again (it would be untypical so early in the game, but if it happens, it happens), you can try to search the internet for solutions ("oblivion savegame corrupt" or similar - there are several entries), perhaps something helps (for example, renaming .bak to .ess in the savegame folder, or disabling autosave, at least when resting, ...).
On the other hand, if you can load the savegame, then you can continue playing (and probably go back to Galaxy, if you want) - I recommend to save often. Savegame corruptions are reported in association with certain places or objects, or with mod conflicts, or with memory-related issues, hard to predict.
Good luck!
My two cents: Installing from the offline installers sounds like a good idea. And I'd try and start from a Windows account that never has seen Oblivion before, just to be sure that there aren't any leftovers from a previous installation somewhere buried in the user's AppData or so. Also, Oblivion's quicksave and quickload functions aren't reliable; users are advised to save solely from the in-game menu, and to load only after restarting the program.
