I think you need to first know what the partial gene sequence is ? This can be done based on similarity search of related sequence of same gene in same species or different species. As the gene sequence has proximal and distal end and if you have already confirmed that your partial sequence is from proximal end then you can start looking at many online software to find your start codon of your partial sequence.
First you need to confirm you DNA Sequence by similarity search using BLAST. After you confirm you gene. You can use the partial fragment in NCBI ORF finder or other related software like MEGA, etc. where you need to specify the codon table and you get the start codon of your partial gene fragment.
Do a BLAST search on NCBI. That should give you an idea. However, complications will arise if you are looking at alternatively spliced transcripts. You may get multiple transcripts that encompass your sequence, yet start / end at different points.
How would you say that your sequence is partial? You can try your sequence with Genscan. It will show that whether your nucleotide sequence possess which type of exon i.e. complete exon, middle exon, terminal exon. If your sequence is middle or terminal exon it wont have start codon.
Thus you can identify the availability of start codon from your sequence.
You can choose the codon preferable table on the basis of source organism. You can find the codon table from the following link: http://www.kazusa.or.jp/codon/