How much would the old Israeli shekel be in US dollars today?

Answer:

The new Israeli shekel was initially valued at 1000 old shekels. Here is an excerpt from another site that is useful.

Israel's original currency was the lira, also known as the Israeli pound, a term which stems from Britain's control over much of Palestine in the 20th century. The original shekel was introduced in 1980 at a conversion rate of one shekel for each 10 lira. In an attempt to control currency devaluation and reduce rampant inflation - which reached an all-time high of 500% in 1985 - the original shekel was replaced with the "new shekel" in 1985 at a conversion rate of 1,000 old shekels to each new shekel.

Here is the link for attribution.

http://converter-currency.com/currency/israeli-new-sheqel.cfm