Can I replace the i3 with an i7 enough though..

The power difference between the i3 and i7 is very small, thus leaving me with the conclusion almost any LGA1155 motherboard will be able to support anything from a LGA 1155 Pentium to an i7.

However, the heat output is another story. Your computer is an all-in-one unit I'm assuming, which has very tight space limitations (also means very little heat tolerance). I would highly doubt you would be able to put an i7 into your computer without it overheating/throttling.

As for RAM, I'm thinking your computer uses laptop-DIMMs. It would be a very easy upgrade so I would highly recommend taking a look at your RAM slots (physically).

Also, on a side note, since this computer is OEM, I highly doubt your Sandy-Bridge based system would be able to accept an Ivy Bridget CPU. Most H61, H67, P67, Z68 boards can accept Ivy Bridget with a BIOS update, however, since your computer is OEM, I highly doubt this is possible.

Regarding an Ivy Bridge Core i7... definitely not. While it can physically fit in the socket, Dell would need to provide you with a BIOS upgrade so that an older chipset can support a newer CPU. There is also the issue of heat since a quad core CPU produces more heat than a dual core CPU does. You would need to install a better heatsink to deal with that heat.

All-in-one PCs are similar laptops. They have very limited expansion capabilities. The best you can hope for is more RAM (maybe) and a larger hard drive or SSD.. That's about it.

As for RAM, you can always call Dell to find out if more RAM can be installed.

65W for dual-core Sandy Bridge vs 77W for quad-core Ivy Bridge vs 95W for Sandy Bridge quads, not much of a difference between dual SB and quad IB.

Dell also makes i5-2400 variants of their all-in-ones and I would make the relatively safe guess that they use the same HSF design to spare themselves the trouble of also maintaining a different chassis design for fundamentally the same PC just like they do with laptops.

Keep in mind Hyperthreading adds a tremendous amount of heat, especially when you're talking about an i7; I would fully expect OP to be able to upgrade to any Sandy Bridget based i5, however, an i7 is a bit iffy. If Dell uses a similar cooler to what Intel uses, then there is a possibility OP may be able to upgrade to an i7, however, I would highly doubt it if they're using some sort of wimpy cooler that they deemed 'good enough' for an i3/i5.

The LGA1155 standard-power i7 (non-S/T) have the same TDPs as the same-generation standard-power i5. 95W for SB, 77W for IB.

So the i7-3770 OP was looking into would still be around 22W less than than an i5-2400 and only 12W more than the current CPU. Unless the i3 is already running unreasonably warm, the IB i7 should be fine at least thermally-speaking.

The main problems are the VRM and BIOS support.

Yes, the TDP of standard SB i5's and i7's are the same, however, Hyperthreading adds a tremendous amount of heat. I'm more concerned about the amount of heat OP's rig can handle rather than the TDP his motherboard supports. With the stock cooler, I saw a difference in temperature of up to 15C on the stock cooler with Hyperthreading on and off.

Best answer selected by StrangeInstance.