I run an mp3 server out of my house 24/7 and don't like interruptions. Verizon DSL is my ISP-internet here has been sporadic since yesterday...Verizon must be having trouble keeping their pcs going in this heat. Anyway, I'm wondering if it would be possible for me to get internet (without jumping on a low wireless bandwidth from my neighbor and without a dial up modem)?

You could look into a different kind of ISP, i.e. cable internet, wireless, satellite, etc. I personally use cable and find it pretty reliable, but you're still at the mercy of the provider to keep things online. When the cable goes out, so does my internet. There's a new wireless company around here called ClearWire that is supposed to be pretty good...

Also, does the server need to be accessible from the internet? Or just from your neighbor? If just your neighbor needs it, you could setup a wired or directional wireless link between the two houses...

My server's on the internet for anybody to get to. Is there anyway I could be my own ISP without a dial up modem?

I suppose. But I'm not sure how. A quick google yielded this site.

Almost all ISPs subscribe to some other ISP (higher up in the heirarchy). Only at the very, very, very, (very!) high levels can you directly purchase an IP block from the IANA/ICANN (this is like the level of Cogent or Level 3 Communications). You will need to use BGP for routing, and create/sign `peering aggreements' with the other large backbone companies (the aforementioned L3 and Cogent). Oh, and you need boatloads of money, lobbyists, lawyers, and market-knowhow. (The point of this paragraph is hopefully to convince you not to attempt this at home.)

That said, there are always more reliable ISPs (and the more reliable they are, the more money you have to throw at them). For example, a T1 line will get you a reliable connection for ~$500/month (but it is pretty slow compared to DSL/Cable: 1.5Mbps symmetric). You can always go up, to partial T3 lines, full T3/DS3 lines, DS{4,5,6,...} lines. You might even want to become your own optical carrier, and have pretty much guaranteed connectivity (as long as your equipment doesn't go out) and good speed (OC-{1,2,3,12,48,192,768} lines). (In addition to the amount of money you have to pay to get internet access/address-space with any of the above methods, you will also have to pay for the initial cost of the equipment, and the cost of maintaining it.)

Now that you know everything that you're not going to get, let me suggest that you go with an ISP geared toward businesses (especiall small business). Here you get very exact contracts that detail how much/little connectivity you are guaranteed (usually with some sort of compensation paid in case of outages) and what speed/data you can use. You may have to pull some strings if you want a business line to your house in a residential district. In terms of providers, some of the same residential providers have much better quality service for business users (e.g., try Verizon Business DSL). Also, another ISP that's catching on quickly with small/psuedo business owners is speakeasy.net (I think this even has a be-your-own-ISP plan in which you provide bandwith to and take money from others). Many ISP's offer small (/29 or /30) IP blocks (you might be able to forget all your NAT-related problems). Some of the newer technologies (i.e., satellites, wireless antennae in big blimps, etc.) might have more speed but have less reliability than any wire-based connection.