To the OP: are you certain that your ticket is really non-changeable? The lowest class tickets originating in Europe are usually non-changeable but those originating in North America usually are, even in N class (albeit with a penalty).

If it really is not changeable and money is more of an issue than time, you can also see whether you can get a cheaper flight to DXB. There is a frequent bus service between Dubai and Abu Dhabi (town centre to town centre) which takes about 2 hours and costs peanuts (or you can get a taxi, which are not very expensive in the UAE).

If you don't mind a low-cost carrier between Istanbul and the UAE, Air Arabia flies to Sharjah (SHJ) (with a connecting bus service to Abu Dhabi) and FlyDubai flies to, well, Dubai, both from Istanbul Sabiha Gokcen (SAW), on the Asian side of Istanbul.