The problem may have been in how you transfered it. You didn't go into much detail. Just be sure to follow the steps in the tutorial below. Note Paragraph 5.
Many libraries worldwide now use Overdrive Media Console, which comes in Mac an Windows versions http://www.overdrive.com/Software/omc . Some find the mobile device transfer process confusing. To load or delete a WMA or MP3 (Macs can only download MP3 books) audiobook onto an Apple mobile device see the "How to Transfer to a Portable Device" video in the guides at Step 7, then do the following.
1. For Windows versions, you must first do a security update of Windows Media Player (even though you won't be using it) using Internet Explorer at http://drmlicense.one.microsoft.com/indivsite .
2. Open iTunes, plug the mobile device into the computer USB port and open the Overdrive Media Console.
3. Highlight the mobile device in the left hand menu of iTunes and insure the "Manually manage music and videos" box is checked in the Summary Tab. If the mobile device storage is full, transfering will delete that portion of music necessary for the ebook.
4. Highlight the book you want to transfer in the Overdrive Media Console and click the Transfer Button. A window opens permitting you to click the boxes for parts of the book you wish to transfer.
5. After the book has been transfered, when you click the disclosure triangle (arrow) to the left of the iPod, iPhone, or iPad in the Device section of the left hand menu of iTunes, MP3 books will show up under the Music subsection and WMA books will show up in the Books subsection. Once the mobile device is disconnected from iTunes, MP3 books will show up in the Songs list of the mobile device and WMA books will show up in the Books list.
6. To remove a book from a mobile device plug the device into the USB port and open iTunes. Click the disclosure triangle to the left of your iPod, iPhone, or iPad in the Device section of the left hand menu of iTunes so that you can see the device’s subcontents. For an MP3 book select the Music subsection, right click on the book and choose Delete. For a WMA book, select the Book subsection, right click on the book and choose Delete.
7. The Overdrive Media Console Guided Tour (videos) is at http://www.overdrive.com/Solutions/Libraries/tour/MenuWelcome.html . The "Portable Devices" and "How to Transfer to a Portable Device" videos are there.
8. To find a nearby library for ebooks search http://search.overdrive.com . You can download the software, search for books and see tutorials without an account at the website of any library that uses Overdrive, however, you need a library card to download books. At this library site, for example, the software and guided tour are at the bottom of the left hand menu.
I just updated my iPhone 3G (10/19/11) and now there isn't any "Books" in the iTunes or Music section of the iPhone so when I tried to transfer the Overdrive WMA book, I received a message "unable to sync" to iPhone and the transfer was unsuccessful.
Is it because of the update. I was always successful before. Now there isn't a "books" in either iTunes or Music -- they are separate. The transfer didn't go into Audiobooks either.
Not sure if this helps because I don't know the rules for iphone 3G but I have an iPhone 4 and I cannot download wma files from Overdrive. I have a mac and I can only download mp3 files. I am not sure if you have a PC. I do know that when I use my old pc I can download mp3 or wma files and can go to my iTouch but on my PC it won't load to my iPhone. Hopefully this will help.