Silver certificate blue seal 1935 E $1

With old bills condition is key to value. We can't see your bill so you'd need to take it to a dealer, I'd get 3 appraisals and ask the appraider what he would offer personally. A worh bill is about $2, crisp $4 but uncirculated up to $18. This bill was still being printed in 1960 so it isn't as old as you might have thought. Here are some auction prices from Wiki
"1935: circulated, $4.-$7.; uncirculated $18.+

1935A: $2.-$3.; $18.+

1935B, C, or D: $2.25-$3.; $13.+

1935E, F: $1.50; $7.+

1935G without "In God We Trust" on the back: $2.25-$3.; $10.+

1935G with "In God We Trust" on the back: $2.25-$3.; $10.+

1935H: $1.50; $7.+"

Read more: http://wiki.answers.com/Q/What_is_the_value_of_a_1935_US_1_dollar_bill_with_ a_blue_seal#ixzz27XJ2eGRl