A Study of LY2940680 in Pediatric Medulloblastoma or Rhabdomyosarcoma

Inclusion Criteria:

* For Part A: Have a diagnosis of recurrent or refractory rhabdomyosarcoma or medulloblastoma and have had histologic verification of malignancy at original diagnosis or relapse.
* For Part B: Have a diagnosis of recurrent or refractory medulloblastoma and have had histologic verification of malignancy at original diagnosis or relapse.
* Current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life.
* Karnofsky score must be at least 50% for participants \>16 years of age, and Lansky score must be at least 50% for participants 16 years of age or less. Participants who are unable to walk because of paralysis, but who are in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score.
* Have fully recovered from the acute toxic effects of all prior anticancer chemotherapy.

  * Participants with solid tumors must not have received myelosuppressive chemotherapy within 3 weeks of enrollment in this study (6 weeks, if previously treated with nitrosourea).
  * Hematopoietic growth factors: At least 14 days after the last dose of a longacting growth factor (eg, Neulasta®) or 7 days for short-acting growth factor.
  * Biologic (antineoplastic agent): At least 7 days after the last dose of a biologic agent.
  * Immunotherapy: At least 6 weeks since the completion of any type of immunotherapy (eg, tumor vaccines).
  * Monoclonal antibodies: At least 3 half-lives of the antibody after the last dose of a monoclonal antibody.
  * Radiation therapy (XRT): ≥8 weeks for local irradiation to primary tumor;≥2 weeks prior to study entry for focal irradiation for symptomatic metastatic sites; ≥3 months for craniospinal XRT, or ≥24 weeks if ≥50% radiation of pelvis; minimum of 6 weeks must have elapsed if other substantial bone marrow radiation has been received.
  * Stem cell transplant: allowed if they have recovered from all acute toxicity and adequate bone marrow reserve is demonstrated. At least 8 weeks must have elapsed since autologous stem cell transplantation or ≥3 months for allogenic transplantation. Participants must be off all immunosuppressive therapy and have no evidence of active graft-versus-host disease.
* Have adequate organ function, including:

  * Bone marrow: Peripheral absolute neutrophil count (ANC) ≥500/cubic millimeter (mm\^3) and platelet count ≥100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions within a 7-day period prior to enrollment).
  * Hepatic: Bilirubin (sum of conjugated + unconjugated)≤1.5 × upper limit of normal (ULN) for age. Serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.0 times ULN for age. Serum albumin ≥2 grams/deciliter (g/dL).
  * Renal: Creatinine clearance or radioisotope glomerular filtration rate (GFR)

    ≥70 milliliters/minute/1.73 square meters (mL/min/1.73 m\^2), or a serum creatinine based on age/gender per the Schwartz formula for estimating GFR utilizing child length and stature data published by the Centers for Disease Control and Prevention (CDC).
  * Neurologic: Participants with seizure disorders may be enrolled if receiving nonenzyme-inducing anticonvulsants and if the symptoms are well controlled. They must have a stable neurologic status for at least 1 week prior to enrollment in the study.
* Must be able to swallow powder or a capsule.
* Have the presence of either measurable or nonmeasurable disease.

Exclusion Criteria:

* Have received treatment within 21 days of the initial dose of study drug with an experimental agent for noncancer indications that has not received regulatory approval for any indication.
* Receiving corticosteroids and have not been on a stable or decreasing dose of corticosteroid for the prior 7 days.
* Receiving enzyme-inducing anticonvulsants.
* Have serious preexisting medical conditions.
* Have current hematologic malignancies or acute or chronic leukemia.
* Have a known active fungal, bacterial, and/or known viral infection, including human immunodeficiency virus (HIV) or viral (A, B, or C) hepatitis (screening is not required).
* Have a second primary malignancy that, in the judgment of the investigator and sponsor, may affect the interpretation of results.
* Have ≥Grade 2 QT prolongation, that is, QTc interval of \>480 milliseconds (msec) on screening electrocardiography (ECG).