ChessHead :
Thanks for the feedback and answers everyone! One of the things I just noticed is that the Athlon II X4 640 does not have integrated graphics like the Phenom x6 did. That kicks the costs of using it above the threshold of just putting the money towards a new system. On top of that, the 640 suddenly seems to be hard to find except from shops that I'm not sure I would trust that the parts were handled properly.
So, maybe I'm looking at a Celeron processor/ motherboard combination now instead. I hate to do that (a bit more of a performance drop than I'd like) but the other options seem to be drying up.
Like Antilli said the IGP (integrated graphics) was not put onto the CPU itself until they released the FM1,FM2,FM2+ socket and the APUs for consumers. With AM3+, AM3, AM2+, AM2 the IGP is actually on the motherboard itself. That is why with those sockets most of the time the really high-end motherboards did not have an IGP yet the mainstream and lower ends had an IGP. If you currently have integrated graphics available with your current motherboard and 1035T then you will still have an IGP with an Athlon CPU. If you can't find the X4 640 anymore you can go with other choices too like Intel.
For your needs I believe FM2+/AM1 and LGA 1150 are all good choices to think about. AM1 being the cheapest.
For LGA 1150 the cheapest option would be the Celeron (~$47) as you said. For AM1 the best would be either of the Quad-Core APUs Athlon 5150 & 5350 (~$50/65). With FM2/FM2+ A8-6600K but at ~$89 it's the most expensive. So so far the cheapest to most expensive is AM1, LGA 1150, FM2/FM2+.
Now for the motherboards. AM1 has the cheapest choices begining at ~$28 and maxing out at $49. One thing to consider is that most of the AM1 motherboards only have 2 SATA ports and a few have 4. If you need more storage connection you will need to choose another socket type or get an addon card for more sata ports. For FM2/FM2+ you have choices from the $43 range to the $100+ range. Finally with LGA 1150 it has motherboards from the $40 range to $100+ range.
If you're thinking of switching motherboard/cpu completely you'll have to decide whether the cheapest lower clocked Quad-Core (Athlon 5150/5350) is a better option than a slightly higher clocked and similarly priced Dual-Core (Intel Celeron) or a much higher clocked Dual-Core (Intel Pentium). Or if the higher clocked AMD Quad Core (A8-6600K) that costs almost double is worth it. All three should have IGP. Next for motherboards you would have to decide how much sata/usb ports you need and the quality/brand of the motherboards. You have time to decide and you can always keep looking for that Athlon too while you're thinking