James -
Welcome and congrats on your new to you Boxster.
I highly doubt it's the ignition. Sounds more like you have a couple of common issues which all reared their ugly head at the same time.
Passenger door window...
Does the window not drop when pulling from the inside handle, outside handle or both? This will help to determine if it's just the door microswitch issue (which one specifically) or the window regulator. Sounds like driver's door is ok, correct?
Top not functioning...
There are multiple causes for this. Most common would be the emergency brake switch. Is the e-brake light coming on when you pull up the handle and the top won't work? If it's not coming on, it's a simple switch which should be replaced. In a pinch you can pull the handle up multiple times, fast, slow, all the way or part way to try and get it to light up.
If the light is coming on, then the next most likely place is the microswitch in the windshield header (where the conv top latches when up). A simple test here is to have the car running and put your finger in the latch hole the top locks into (there will be a metal cover you'll push in and fell slightly click). Now, roll your windows up all the way. Remove finger from hole. Do both windows drop? Test repeatedly - do windows drop each time? If so, should be good here as well.
Finally, the next most likely culprit could be the relay for the top in the footwell. It's the only double sized relay. When the top won't open or close, try to tap on it a few times to see if this actuates it.
There are a couple of other possibilities but these are the more common ones so please test or let us know more of the symptoms or results to test above.
Boot opening...
B/c we have a language difference, what specifically are you calling the boot? Front hood/trunk cover, rear trunk/hood or clamshell for the convertible top. On a '98, front hood is 100% manually driven/opened. Rear has a manual release as well as electrical/remote from key fob actuating a motor. Clamshell is mechanical but driven in unison w/ the convertible top. Please explain more.
Sounds like you have a good warranty which should cover most of these issues. As such, you should only have to pay the deductible if any on the repairs. If your warranty doesn't list the above as covered, then not to worry, most of us have seen these issues before and give you instructions or links on how to fix it yourself...even if you're not 100% comfortable w/ tools.
Please let us know the answers to the above and we can help you further so you don't get taken advantage of from the repair center.