Assets
Current standards say the Mayday should be broadcast on VHF channel 16 (156.8 MHz). A 1999 phone, probably on 2g would likely use 900MHz (UHF). The slightly broken comms unit in the pod is probably using channel 16 or equivalent*. This is your first problem. The patrol ship will be listening in for signals broadcast on the mayday frequency. That's the frequency you need to hit, so first up is rebuilding your phone to that frequency.
Or you could look at the pod comms system and see what's wrong.
Your next problem is that your mobile phone's range is laughable in interstellar space. What's going to be even more laughable is when you try to use it in the radiation shielded environment of your escape pod. The signal, which is line of sight at the best of times, most likely won't even penetrate the hull. So now you need to hook it up to the external antenna used by the pod's own comms system.
Or you could look at the pod comms system and see what's wrong.
Now you need to make sure you're using the right broadcast method: are you on AM or FM? (There's no reason to think that 100 years from now they'd be able to pick up an analog signal)
I'm sure you can see where I'm going with this. Fix the pod.
Ultimately all you're going to do is rebuild a copy of the pod's own comms system with a batch of obsolete components. If you're good enough to do that you're good enough to fix the pod's own system which will be much easier.
*I mention channel 16 as an example to show that there are standards for distress signals and they're very different from the standards for mobiles, if you want someone to pick it up then you need to be broadcasting on a frequency they're listening on.
Distress frequencies
2182 kHz forms an essential part of the Global Maritime Distress Safety System (GMDSS). It has an associated DSC frequency at 2187.5 kHz. Other international distress frequencies, in use as of 2008, include:
121.5 MHz - civil aircraft emergency frequency
243 MHz - military aircraft emergency frequency
156.8 MHz - Marine VHF radio channel 16, short range maritime use
406 MHz / 406.1 MHz - Cospas-Sarsat international satellite-based search and rescue (SAR) distress alert detection and information distribution system
Discontinued frequencies
500 kHz Morse code is no longer monitored.
121.5 or 243 MHz locators. (No longer automatically monitored by satellite, though still used for aircraft communication and short-range direction finding.)
Effective 1 August 2013, the U. S. Coast Guard terminated its radio guard of the international voice distress, safety and calling frequency 2182 kHz and the international digital selective calling (DSC) distress and safety frequency 2187.5 kHz. Additionally, marine information and weather broadcasts transmitted on 2670 kHz terminated concurrently.