Do you know the sequence of any part of the gene?  Maybe you could walk down the chromosome from a known or predicted point in short sequencing reactions until you get to the unknown region.  

Thanks

I just know one contiguous sequence of 900 nucleotide 

Best

T

if you want the entire gene you will have to go back to source and get some rna and make a cDna and use inverse pcr to generate the cdna sequence  and from that the genomic sequence around the exons otherwise you will have to blast the sequence that you have and make assumptions for similar species and genes to try to generate some form of consensus gene which may look like the correct gene for your species

would next generation sequencing give you the answer quickly?

I agree with Paul Rutland. If you cannot get RNA then it will be impossible to know if you have missed a 5' non-coding exon, or to be sure where the 3' tail ends.  Other than NGS, or resorting to making a BAC library and selecting with your 900bp fragment, I have  one suggestion, which is to use  an indirect amplification technique to get some of the sequence.

Align the sequence of this gene from all species for which it is known and look for conserved regions in  which there are a maximum of about two or three polymorphisms in a 20 bp exon. Use these conserved areas(with appropriate variant bases to cover the inter-species SNP's, to produce core sequences of each exon or as many as you can get. You can also try to PCR between exons using these sequences.  To get some more sequence cut genomic DNA with one or more restriction enzymes to produce fragments that are of a target size that should be easy to PCR ideally 500 - say 2000bp. You can do a partial cut to get  most of your DNA to the right size if needed, or alternatively sonicate to size and "polish" the ends. Now ligate a unique amplification sequence onto the cut ends (E.g. in T7 or M13  primer sequence). Amplify in a first round with the antisense of this primer plus a primer derived from your alignments with a different specific 20bp secondary primer sequence attached to its 3' end.  In a second amplification use the antisense of this 20bp sequence first primer. Sequence your fragments and add to  the phylogenetic alignment. This is  a quick and dirty way of getting a first look.

Could the easiest way be to produce a probe from the 900 known sequence to capture RNAs from a cDNA bank, sequence the captured sequences and with 5'RACE fill the gaps?

You could try inverse PCR using the short exon as target. Of course it depends on the gene length if you will be able to amplify the whole gene or not, but with multiple rounds you can succeed. 

The best

Massimo