I just bought a new HP Pavilion g7 laptop that's got an AMD A6-3420M APU w/ Radeon HD graphics. It's CPU is a AMD quad core that does 1.50 GHz w/ each core. With Turbo Core technology, it can go up to 2.4 GHz. I've read this link that it does turbo core automatically: http://www.anandtech.com/show/3641/amd-divulges-phenom-ii-x6-secrets-turbo-core-enabled

Anyways. Will this new laptop I got perform better than my old AMD Dual-Core 2.5 GHz? Will it work with DOSbox better? DId I made the right choice getting a computer w/ a powerful processor.

If your old CPU vas a Turion II M620, the A6-3420M offers about 50% more CPU power ( at least that's what the benchmark say ). In addition, you probably have a vastly improved GPU .
The frequency is not what actually matters in this case. The cores are more efficient and the L1/L2 cache of the A6 is superior to the Turion's

I use an A8 based laptop. Although I wouldn't label it as a powerful processor ( It's somewhere between a sandy bridge I3 and a first gen i5 ) , It's quite good for most games but I encounter problems from time to time with older games. In most cases, I was able to solve this by switching from dual graphics to the integrated GPU.

The only one that I could not solve at this stage is Alpha Centauri. The game simply won't accept the CPU and will crash at the end of the first turn.

Erm, not meaning to sound nasty - but shouldn't you have asked these questions _before_ buying it?

GHz has not been a reliable measure of performance for some time - so don't worry too much about that. On the other hand 4 core is not (always) twice as fast as dual core. The software has to be developed specifically to make use of it. On the other other hand, quad core means more things can go on at once before you notice a slow down.

DOSBox games will almost certainly _not_ be using more than one core.

In my opinion (and I'm prepared to be shot down here) the performance of DOSbox games is not so much to do with the raw oomph of your system, it is more to do with differences in architectures (both hardware/drivers and OS) between systems when the games were developed and current systems (and specifically _your_ system). Obviously this only holds true beyond a certain point - too little oomph is too little oomph.

This is why matching the DOSBox configuration between your system and the game can be so important.

I wouldn't call it "powerful", but it should indeed perform better than your old one. The difference should be most noticeable for modern games which either depend a lot on good graphics, or which make use of more than 2 CPU cores. DOSBox games are probably the category where you'll be seeing the smallest improvement, since these use neither the additional cores nor the better graphics.

My old laptop is a HP Pavilion DV7-3160US 17.3-Inch Laptop and it does use a AMD Turion II Ultra Dual-Core Mobile Processor M620 (2.5 GHz, 2 MB L2 Cache).

If the benchmarks can be trusted, this should offer something like 50% CPU and 30% GPU performance improvement. Your config is more than enough to run Dos Box games, but the atypical hybrid crossfire might sometimes make it a bit more difficult.

If you're using the latest OS on your laptop then the quad cores will improve performance. Programs which require non-linear processing power such as video editing, graphics editing, and games will show vast improvement. DOSBOX and the DOS games are such old programs the performance will be based on backwards compatibility and slowing down the game, not core performance (which would play the games much too fast if left without configuring DOSBOX).