The two solutions are too far apart to be considered similar. The issue is that a factor of 1/2 is missing from the pdf definition. To match the likelihood the pdf needs to be

pdf[x_] := 
  Sqrt[(1 - \[Rho])/\[Rho]]
    Exp[(inN[x]^2 - ((Sqrt[1 - \[Rho]] inN[x] - inN[PD])/
        Sqrt[\[Rho]])^2)/2];

Now the result will be

{PD -> 0.013438593418697627473, \[Rho] -> 0.10995316859509961784}

which matches

{137.731, {PD -> 0.0134386, \[Rho] -> 0.109953}}

I continue to make more than my fair share of programming mistakes (especially with Mathematica). The only ways I know how to minimize such occurrences are to (1) perform lots of checks (Do the probability functions sum/integrate to 1 for arbitrary parameters?), and (2) (probably the best technique) Grab anybody and explain your problem with the code in front of both of you. Then either that person will catch the obvious (upper/lowercase, spelling, etc.) or while you're explaining you'll say "Oh, nevermind." because the issue will become obvious.

See also:

http://mathematica.stackexchange.com/questions/6498/standard-errors-for-maximum-likelihood-estimates-in-finddistributionparameters

and

http://community.wolfram.com/groups/-/m/t/201528

Cheers,

M.

Jim,
Suggestions can be sent via http://www.wolfram.com/support/contact/email/?topic=Technical

A simple code example with actual output and preferred output would help clarify the issue.