Hi beedup, welcome to the forums.
My reply is a little long, but I hope that doesn't scare you off.
I can't really help with regard to sources as I'm not sure where you are. There are, of course, lots of on-line places you can get LEDs and solar panels from, as well as physical shops you can go to, like (maybe) Radio Shack. But I'm not well versed with all of them.
As to your project, there is only the Freelight that Saaby mentioned which uses LED as well as a solar panel. There are a few emergency lights out there that have a solar panel but use incandescent bulbs. Not a big deal to modify those to take LEDs, especially the lower voltage yellows. The higher voltage whites will require a small booster circuit of which there are many to choose from. One of the simplest, and my favourite, requires only a few standard components and not all those hard to find IC chips. It does require you to hand wind your own inductor though, which can get a little fiddly. Search the forums for the key word "SatCure". You can also look for the Brinkman circuit which uses a few more components, but uses a standard inductor.
Building your own solar-powered flashlight from scrap will require a little thought as to the final function. Is it going to be handheld or stationary? How long does it need to run, whole night or intermittent use? Separate charging station or built-in solar panel? How much direct sun does your location usually have?
The amount of direct sun your charging location has will determine how big the panel needs to be. The panel must be rated to provide slightly higher voltage than the batteries that you are using. Go for about 0.5V to 1V over what your batteries deliver. Next, figure out how much current the batteries can take during recharging. Some of the more knowledgeable folks will probably tell you what the safe rates are. I think it is between 200mA and 500mA for NiMH depending on whether it is a quick cycle or slow cycle charge, but I could be wrong. This will tell you how much current you will need from the panel.
BTW, realise that you need direct sun on the solar panel to achieve the rated voltage and amperage. Voltage and amperage will drop off as you get less sun on your solar panel. Amperage will drop faster than voltage. If you don't get the rated current, it is no big drama as it merely means that you can't complete the charging cycle in the stated time. But if you can't get the required voltage, your batteries will not charge. So if you are in a location that has lots of cloud cover or is shaded, consider getting a panel that can deliver much higher voltage and amperage, then installing a circuit to regulate the voltage. Alternatively, there is a circuit somewhere abouts that will boost and regulate the voltage to the required amount from any given panel, but with proportionate reduction in delivered current.
When you consider the batteries, you need to figure how much capacity is required and the voltage that needs to be delivered. Your standard Nichia 5mm LEDs will typically be run at 4.0V 40mA for maximum brightness without blowing up the LED. So (power = voltage x current) each LED takes approximately 160mW of power, or 640mW for your bunch of 4 LEDs. Multiply that by the length of time you expect your lamp to operate. This will give you milliWattHours. Batteries are rated in voltage and mAH (milli-amp hours). So you can figure how large the capacity of your batteries should be. BTW, discharging your batteries completely is bad for them, so give an allowance, like 25% extra capacity or so.
How you arrange the LEDs will also determine the batteries that you use. Parallel, series or pairs? LEDs are current driven devices. Hence, if you want them all to be of the same brightness, you should run them in series so that all of them get the same current. But 16V batteries are a little hard to come by. You could, I think, get 18V batteries which should work fine. Alternatively, have them in pairs using 9V rechargeables, or in parallel with 3 batteries of the 1.5V variety in series.
Ultimately, it is up to you to determine the best combination to suit your conditions. I hope all that rambling helps you. And do post any further questions or clarifications you require.
