If you can only maintain a boil with the pot covered, don't bother brewing. You can cover the pot to achieve the boil, but once it starts, you want to take the cover off and let it steam. A lot of undesirable chemicals evaporate out during the boil, so keeping it covered will definitely affect your beer's flavor. 2 hrs+ is pretty unacceptable in my book. My gas stovetop did the job in less than half of that. My turker fryer cut that in half again, and my new burner (see signature) will vigorously boil 16+ gallons in 15-20 minutes.
The bottom line: I suggest a partial boil for this one.