Try changing

contracts['CrowdFunder'].contract.contribute({
    value: web3.toWei(0.000000000000000005, 'ether')
});

to

contracts['CrowdFunder'].contract.contribute({
    value: web3.toWei(0.000000000000000005, 'ether'), 
    gas: 100000 
});

Refer to the example under Contract Methods in JavaScript API - web3.eth.contract.

And modifying the call as suggested by eth's comment below:

contracts['CrowdFunder'].contract.contribute({
    value: 5, 
    gas: 100000 
});

start(...) and start1(...) are two ways you can rewrite your function to work as expected:

pragma solidity ^0.4.0;
contract Ballot {
    struct Escrow {
        address thirdParty;
        address seller;
        address buyer;
        uint amount;
        address recipient;
        uint status;
    }
    uint numEscrows;
    mapping (uint => Escrow) escrows;

    function start(address seller, address thirdParty) returns (uint escrowId) {
        escrowId = numEscrows;
        numEscrows++;
        Escrow memory e;
        e.thirdParty = thirdParty;
        e.seller = seller;
        e.buyer = msg.sender;
        e.amount = msg.value;
        e.recipient = seller;
        e.status = 1; // started

        escrows[escrowId] = e;

        return escrowId;
    }

    function start1(address seller, address thirdParty) returns (uint escrowId) {
        escrows[numEscrows].thirdParty = thirdParty;
        escrows[numEscrows].seller = seller;
        escrows[numEscrows].buyer = msg.sender;
        escrows[numEscrows].amount = msg.value;
        escrows[numEscrows].recipient = seller;
        escrows[numEscrows].status = 1; // started
        numEscrows++;
        return numEscrows;
    }
}

And here is the Solidity realtime compiler and runtime screen showing that both start(...) and start1(...) execute without throwing an exception:

Note that start1(...) costs less gas than start(...).

In start(...), I added the memory keyword - see What is the memory keyword? What does it do?, Difference between Memory and Storage? and What does the keyword "memory" do exactly? for further information.

In your question, you mentioned "The only array there is escrows[] declared as mapping (uint => escrow) escrows;". Note that arrays are different from mappings - see Arrays vs Mappings and Store data in mapping vs. array.