The purpose of this study is to determine the dose regimen of Ispinesib in combination with carboplatin in patients with solid tumors. Ispinesib is dosed by 1-hour intravenous infusion and carboplatin is dosed by 30 minute intravenous infusion every 3 weeks (on the same day). A patient may continue to receive treatment as long as they are benefiting from the treatment. Blood samples will be taken at specific times to measure the amount of both drugs in your body at specific times after the drug is given. Blood samples will also be taken for lab tests such as complete blood counts and clinical chemistries. Physical exams will be performed before each treatment with Ispinesib. During the treatment phase, the patients will undergo regular assessments for safety and clinical response.