http://ark.intel.com/products/40739/Intel-Pentium-Processor-T4400-1M-Cache-2_20-GHz-800-MHz-FSB-Socket-P
If it's socket P, then it should be upgradeable. However, a quick google search says that model shipped with a Pentium T4400. You really should consider buying a newer laptop.
Even though the T4400 is a "bargain" CPU, it's also one of the later CPUs Intel put out from the Core 2 Duo series. The main difference between it and a full-blown Core 2 Duo is that it has 1 MB of cache instead of 2 MB. So you're unlikely to see any huge performance gains from an upgrade. The Notebookcheck benchmarks show only about a 15%-20% improvement if you were to upgrade to a T9300. The clock speed alone (2.5 GHz vs 2.2 GHz) accounts for 14% so there's very little performance improvement to be had from upgrading the CPU.
http://www.notebookcheck.net/Intel-Pentium-Dual-Core-T4400-Notebook-Processor.25726.0.html
http://www.notebookcheck.net/Intel-Core-2-Duo-T9300-Notebook-Processor.26538.0.html
Also, the SSD probably hasn't helped much because laptops this old typically only have SATA 1, which goes up to 150 MB/s. Modern SSDs typically reach 450-550 MB/s. The laptop probably also doesn't support AHCI, which is needed if you want NCQ (allows the drive to handle multiple data requests simultaneously). That's where SSDs get the vast majority of their speed when reading small files. So the SSD's performance is being badly bottlenecked by the laptop. Combine this with the small edge to be gained from a new CPU, and you are really better off getting a new laptop.
However, if you insist on upgrading, for the upgrade to work:
■ the BIOS must support the new processor. Download and install the latest BIOS from Toshiba. The readme often says which new CPUs are now supported, which may give you a hint as to which CPUs might work.
■ the FSB (800 MT/s in your case) must be the same on the new CPU. This isn't strictly true - most motherboards support multiple FSB speeds. But if you don't know what speeds are supported, getting a CPU with the same FSB has the best chance of working.
■ the TDP (35 Watts in your case) should be the same or lower. If you use a higher TDP CPU, the cooling system in the laptop may not be able to cool the system sufficiently. This one also isn't strictly true because manufacturers often take a chassis designed for a high power CPU, then sell a discount version with a lower power CPU. So the laptop's cooling system may be able to handle a higher TDP. But unless you know for sure, you have to play it safe and stick with the current TDP - you know that works.
Aside from that, it's buy a new CPU from eBay which seems like it would be compatible, install it, and cross your fingers.
http://en.wikipedia.org/wiki/List_of_Intel_Core_2_microprocessors#.22Penryn.22_.28low-voltage.2C_45_nm.2C_Small_Form_Factor.29
As for memory, open up task manager (right-click the task bar and click on task manager from the popup menu). Switch to the performance page. The memory graph should show you how much RAM is currently being used, and just below that how much physical RAM is available (it's a bit less than what's actually installed due to the integrated video reserving some). If you've got about a half or 3/4 GB difference or more between used and physical RAM, then adding more RAM is not likely to help. Frankly the extra $25 for a new 2 GB RAM stick would be better spent applied to a new laptop.
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