I've had this happen before in my analyses. This is often the result of an unflagged error in your input file - codeml generates a pairwise matrix, one of the initial steps, but doesn't proceed to the ML estimation of omega. I had this happen a while back when my sample names did not conform exactly to Phylip specifications and again when my samples started with a number. My first suggestion would be to shorten the names to 10 characters or less and see what happens. This is easily accomplished with sed:

cat YOURFILE.fa | sed -e s/Updated_Gene_HN//g > YOURFILE.renamed.fa

This reads the file, finds every instance of "Updated_Gene_HN" and replaces it with nothing, globally, then writes the result to a new file. This can be iterated easily in bash, too, if you need it.

I also needed to do some single-rate (i.e., global) omega calculations a couple of weeks ago. I'm pasting my control file below, though it looks like yours is fine. This file executed over 15,000 times, so I'm confident it works :). I've changed the names of the seqfile and outfile; I also provided my own tree.

seqfile = FASTAFILENAME * sequence data filename
treefile = tree.phy * tree structure file name
outfile = FASTAFILENAME.codeml * main result file name
noisy = 9 * 0,1,2,3,9: how much rubbish on the screen
verbose = 1 * 0: concise; 1: detailed, 2: too much
runmode = 0 * 0: user tree; 1: semi-automatic; 2: automatic
* 3: StepwiseAddition; (4,5):PerturbationNNI; -2: pairwise
seqtype = 1 * 1:codons; 2:AAs; 3:codons-->AAs
CodonFreq = 2 * 0:1/61 each, 1:F1X4, 2:F3X4, 3:codon table
* ndata = 1
clock = 0 * 0:no clock, 1:clock; 2:local clock; 3:CombinedAnalysis
aaDist = 0 * 0:equal, +:geometric; -:linear, 1-6:G1974,Miyata,c,p,v,a
aaRatefile = dat/jones.dat * only used for aa seqs with model=empirical(_F)
* dayhoff.dat, jones.dat, wag.dat, mtmam.dat, or your own
model = 0
* models for codons:
* 0:one, 1:b, 2:2 or more dN/dS ratios for branches
* models for AAs or codon-translated AAs:
* 0:poisson, 1:proportional, 2:Empirical, 3:Empirical+F
* 6:FromCodon, 7:AAClasses, 8:REVaa_0, 9:REVaa(nr=189)
NSsites = 0 * 0:one w;1:neutral;2:selection; 3:discrete;4:freqs;
* 5:gamma;6:2gamma;7:beta;8:beta&w;9:betaγ
* 10:beta&gamma+1; 11:beta&normal>1; 12:0&2normal>1;
* 13:3normal>0
icode = 0 * 0:universal code; 1:mammalian mt; 2-10:see below
Mgene = 0
* codon: 0:rates, 1:separate; 2:diff pi, 3:diff kapa, 4:all diff
* AA: 0:rates, 1:separate
fix_kappa = 0 * 1: kappa fixed, 0: kappa to be estimated
kappa = 2 * initial or fixed kappa
fix_omega = 0 * 1: omega or omega_1 fixed, 0: estimate
omega = .5 * initial or fixed omega, for codons or codon-based AAs
fix_alpha = 1 * 0: estimate gamma shape parameter; 1: fix it at alpha
alpha = 0 * initial or fixed alpha, 0:infinity (constant rate)
Malpha = 0 * different alphas for genes
ncatG = 8 * # of categories in dG of NSsites models
getSE = 1 * 0: don't want them, 1: want S.E.s of estimates
RateAncestor = 0 * (0,1,2): rates (alpha>0) or ancestral states (1 or 2)
Small_Diff = .5e-6
cleandata = 0 * remove sites with ambiguity data (1:yes, 0:no)?
* fix_blength = -1 * 0: ignore, -1: random, 1: initial, 2: fixed
method = 0 * 0: simultaneous; 1: one branch at a time
* Genetic codes: 0:universal, 1:mammalian mt., 2:yeast mt., 3:mold mt.,
* 4: invertebrate mt., 5: ciliate nuclear, 6: echinoderm mt.,
* 7: euplotid mt., 8: alternative yeast nu. 9: ascidian mt.,
* 10: blepharisma nu.
* These codes correspond to transl_table 1 to 11 of GENEBANK.

I hope this resolves your issues. Please respond if you need more help - I use codeml all the time.