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Is this the original Galaxy S? (Look under the battery on the phone, is it the GT i9000?).
Ok, there are a couple things wrong here and they vary from minor to major. No matter what it is though, we can resolve it (as long as its not a hardware failure, which is rarely ever is).
Lets just start with the easiest fix, and if that doesnt work we can move on.
If the same issue occurs, let me know and we will continue.
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You used whats called the Recovery Partition, it becomes much more usefull if you're rooted, as you use it to flash new versions of Android onto your phone. For instance, all hour of the Galaxy S's I have all are running Android 4.03 Ice Cream Sandwich.
But, about the phones problem. Unfortunately, if you used the recovery to clear the cache partition and it still wont boot then there is an issue with corrupt data either in the kernel or the OS itself and we will need to reset it to fix it.
As long as you have a Google account synced to your device, your contacts, calendar, etc. will be re-synced to the device after you run the initial setup again as long as you sign in with the same Google/Gmail account. Any apps you have paid for, you can get back after you reset the device by opening the Market, pressing Menu on the phone and choosing "My Apps".
As far as any data that is stored on the SD Card(images, music, etc.), it will not be erased. Only the phones internal memory is formatted.
To complete a Factory Reset follow the same directions I gave you before, but choose Wipe Data/Factory Reset from the menu instead. That will restore your phone to an out-of-the-box condition, resolving whatever the prroblem is.