Note that you will need to check the gmail (or maybe googlemail) account that was used when you set up your phone.
To find out what this was go into Settings and under Accounts, tap Google. The top section of the next screen is Accounts and this shows the account name your phone is using and whether sync is turned on or off.
If you tap the gmail/googlemail address you will get a number of options, one of which is Contacts with the note Touch to sync now. Touch it to sync now.
Once you've done that, you can go to your computer, fire up a browser, log into gmail using the account name you found above and you should be able to find your contacts. Can't tell you how to do that coz I rarely use gmail so can't recall where to find contacts - unfortunately, finding things in gmail is a complete PITA.