Your basis applies to the two traditional IRAs in aggregate. However, the first problem you have is that many of the nondeductible traditional IRA contributions were not properly reported on Forms 8606 for the years for which the contributions were made. Generally speaking, the IRS does not recognize basis that was not been properly reported on Forms 8606.
Yes, part of your Roth conversion was a nontaxable distribution of basis in nondeductible traditional IRA contributions. However, the reporting on your 2010 Form 8606 was incorrect because an incorrect amount was reported on line 6. Using a $14,000 as the value of IRA 1 at the end of 2010 (it was probably larger unless these funds were at some point moved to IRS 2, but I'll use $14,000 for the example calculation) and treating your basis in 2010 as being only $4,000, the amount of the Roth conversion treated as nontaxable should have been $4,000 * $60,000/ $134,000 = $1,791. However, having claimed that $4,000 of your basis applied, you are not now permitted to take an inconsistent position that only $1,791 should have applied and that you now have $2,209 of basis remaining.
How is it that the tax preparer made so many errors?
Reconstructing your basis correctly might be a lost cause. You would have to file the five missing Forms 8606 (probably subject to a $50 penalty for each form that was failed to be filed timely unless you can show reasonable cause) to establish that you had actually made the $10,000-worth of nondeductible traditional IRA contributions. Correcting the 2010 Form 8606 is probably not possible due to the statute of limitations, so you would have to continue to treat it as having consumed $4,000 of your basis.
