Initially, in the 4th cohort (dose level 4), a minimum of three patients will be enrolled. If 1 of the 3 patients experiences a Grade 3 (or higher toxicity), the cohort will be expanded to 6 patients. However, if 3 patients complete one cycle at the assigned dose regimen without experiencing a Grade 3 (or higher toxicity), enrollment in the next cohort (dose level 5) can begin. This scheme will apply to cohorts 4, 5, and 6 MTD is defined as the highest dose of ABT-751 given in combination with carboplatin at which fewer than 33% of patients experience DLT. MTD will be evaluated at the end of the first cycle (21 days). Toxicities will be determined also at the end of cycle 2 to evaluate the safety of combining both agents on day 1. If the MTD has not been determined after completion of the 6th cohort (dose level 6), based on an overall review of toxicity at each cohort, the Investigator may select a dose thought to be the recommended dose for Phase 2 studies. Six patients treated at MTD will undergo PK and PD evaluation. An additional cohort of 14-20 patients will be enrolled at either the MTD or at the recommended Phase 2 dose level administering both drugs on day 1. During this portion of the study patients will be withdrawn from the study if any of the following occur: