Don't confuse problems with a phone system and voip. The first thing you want to do is figure out what's wrong with your phones. In today's climate, a 24 extension Partner system is really inexpensive, about 1/3 the price of a new VoIP system and you already own at least 50% of a working Partner. It may be that you just need a single part to repair it. You may also look into a different phone system that uses standard phones. Don't let your present phones be the deciding factor, new speakerphones with message waiting are only $35 each. We have several accounts with Panasonic TDA-100 and 200 systems that have all the features but PMS and that can be added at any time via an external program.
Now, the VoIP carriers may be useful in giving you flat rate or low-cost long distance. You might benefit from installing VoIP or alternative lines for calling...provided you have a way of billing for the additional expense. You're not going to slap 4 or 8 VoIP lines on a 128K up DSL and expect quality, but two lines might work and it would be all you'd ever need for 20 rooms.
Above all else, keep in mind that it will always be cheaper to repair than replace. I never ask what type of phone system a motel has. I ask about the Internet. I stay in motels about 8 nights a month and I can't even remember the last time I used the phone in a room. But, as I sit in a Super8 answering this post, I surely can tell you where the wireless access points are.
Hope this helps.
LkEErie