There is a hard drive which I suppose some may call a hard disk and then there is Random Access Memory (RAM). If your hard drive fills up it can affect processing but you will get a warning of low disk space. You need RAM for programs to run. For 32 bit W7 2GB is recommended, 1GB is the minimum and 4GB is the maximum (of which only about 3.25GB can actually be used). For 64 bit W7 3GB is recommended and the max is generally limited by your motherboard.
Your CPU processes the command instructions of the programs which are in memory (RAM). If the RAM fills up, portions of memory may be swapped out to the page file on the harddrive. If there is excessive swapping in and out between the RAM and the pagefile such that it effects processing time, this is called Thrashing. Now with W7 (and Vista) the system is supposed to utilize free CPU and memory to do things such as search indexing, etc so it may appear as though your CPU is overworked while in fact it is just the OS utilizing available resources.
If you have less than 4 GB of RAM and you can afford it then it isn't a bad idea to buy some more. If your HD has less than 40GB free, I personally would buy an extra HD. If you post back with whether you mean CPU, RAM, or harddrive and what utility you are using to determine it's maxed-out status we might be able to offer further advice/recommendations.