All the entries and exits are in the old passport. Will they still be able to track my ins and outs with the new passport? How can I prove I was present if I don't have my expired passport?
If you have a history of travel during your eligibility period and you have lost that very passport, be prepared for non-routine processing. While you won't be the first person who has lost a passport, you better have VERY strong evidence to match the dates you are showing as 'days in Canada'. Employment letters/ salary slips/ T4s/rental agreements/ mortgage papers are all good indicators of presence but not 100% foolproof. If you were self employed and not an employee of a known corporation who can be contacted to verify your presence, your case could perhaps take significantly longer.
A stamp on your passport is merely an indicator that you were in Canada on that particular date - it is the in between period that is critical to be supported by evidence and that is where some of the documents mentioned above come in handy. An employment log - in some areas of work you have to time in and time out, could go a long way in establishing presence in Canada. If employed, check with your HR on what documents they can give to corroborate the dates you are claiming to be in Canada.
If any of your travel during the period is to countries that stamp your passport in non Eng/Fr, you will need certified translations of each of those stamps. Unlikely a translator will certify those without seeing the original. So as
@wink says, you may want to wait out and relook at your eligibility period.
If none of the above work for you, start praying