I have a bit of experience in this and my understanding from this is as follows:
If you think you have a manual penalty dont change anything and put in a reconsideration request. Within a week you should have a reply saying your site still violates the google guidelines. If you get this reply then I belive you can be fairly sure you have a manual penalty. The reasoning behind this is that when a reconsideration request is put in it will be automatically checked against a list of manual penalties if your site is on the list it will be passed onto a human or specific automated check for compliance with the rule break and replied to accordingly.
I have found that reconsideration requests for algo penalties tend to get ignored - no reply. Automated penalties mean check for the obvious stuff that an algo could pick up, keyword stuffing etc.
Assuming a manual panalty you could put in a second/third request wait another week for the reply to come back that it has been reviewed then cross reference your server logs to find the exact page google are looking at to give you some clues - this is a HUGE job and only works depending on your site setup. You might also find you annoy google and increase your penalty if no action has been taken each time (assuming a human and not specific automated check).
The second option for a manual penalty is to wait, these tend to be time based so your site should reapear within 30 to x number of days. However you then could have the penalty re-imposed.
From what I understand the reconsideration request only speeds up the process of getting back into the results if the violation has been fixed, otherwise you have to wait out the time penalty. Ie with a manual penalty you could never put a reconsideration request fix the problem then be back in the serps after 30 days when the penalty expires without any further problems. However with a reconsideration request if the problem was fixed on day 1 you could be back on day 7-10 so 20 days earlier.