How can I ............?

So I unearthed my mom's really old Keds the other day, they're white, and unfortunately really dirty: a href="http://www.google.com/imgres?imgurl=http://ny-image0.etsy.com/il_570xN.148036072.jpg&imgrefurl=http://www.etsy.com/listing/48420992/simple-and-dirty-white-vintage-keds&usg=__sDgW8hB0QVNzjw0qjxEPB8w0=&h=383&w=570&sz=20&hl=en&start=45&zoom=1&tbnid=LLXHZpbZgwH_CM:&tbnh=143&tbnw=191&ei=Fpe0TZaYA8mjtgf0sZHqDg&prev=/search%3Fq%3Dreally%2Bdirty%2Bwhite%2Bkeds%26um%3D1%26hl%3Den%26biw%3D1040%26bih%3D774%26tbm%3Disch&um=1&itbs=1&iact=rc&dur=559&page=3&ndsp=21&ved=1t:429,r:9,s:45&tx=156&ty=96" rel="nofollow"http://www.google.com/imgres?imgurl=http…/a (they look like that except with orange-y dir stains along the top parts of the shoe, the laces, etc. I scrubbed them with shaving cream, body wash, and whitening toothpaste and windex and they look a little better, I don't have a washing machine available but I want to know how to at least get rid of those nasty dirt stains be tomorrow, if not also restoring it to it's almost brand new white state (the Keds are yellowing as well as the dirt stains) and there's only one bright white spot, the original color of the shoes, so it looks kind of weird and I am afraid people will call me out on my shoes. So how can I clean my Keds and make them white and shiny, if not just stain free? Thank you.